Defendant-Appellant Glen Benussi was found guilty after a jury trial in the United States District Court for the Southern District of New York (Lewis A. Kaplan, Judge) of conspiracy to commit securities fraud, see 15 U.S.C. §§ 77q(a), 77x, wire fraud, see 18 U.S.C. §§ 1343, 1346, and commercial bribery, see 18 U.S.C. *611§ 1952(a)(3), in violation of 18 U.S.C. § 371. He now appeals from a final judgment of conviction pronounced on July 8, 2002, and entered on July 29, 2002, sentencing him to five years’ incarceration, a three-year term of supervised release, $10,773,461.24 in restitution, and a $100 special assessment. Benussi is presently released on bad pending resolution of this appeal.
In urging this court to reverse or vacate his conviction, Benussi does not dispute his knowing and intentional participation in the charged conspiracy. Instead, he challenges the legal and factual sufficiency of proof that the conspiracy operated within five years of his May 7, 2001 indictment, as required by the applicable statute of limitations. See 18 U.S.C. § 3282(a). Presented with substantially this same challenge in a post-verdict motion for a new trial, see Fed.R.Crim.P. 33, the district court concluded that the statute of limitations was satisfied by evidence that Benussi’s co-conspirator, Louis Pasciuto,1 had received fraud proceeds on and after May 8, 1996. See United States v. Benussi, 216 F.Supp.2d 299, 317 (S.D.N.Y.2002).
In challenging this ruling on appeal, Be-nussi argues that (1) Pasciuto’s passive receipt of fraud proceeds cannot, as a matter of law, establish the conspiracy’s continuance into the limitations period; (2) the trial evidence was, in any event, insufficient to prove Pasciuto’s knowing receipt of such proceeds; (3) the prosecution’s reliance on Pasciuto’s receipt of proceeds, an overt act not charged in the indictment, constituted either an impermissible constructive amendment of the indictment or a prejudicial variance in proof; (4) the Fifth Superseding Indictment on which Benussi was tried, see United States v. Fiore, S5 00 Cr. 1267(LAK) Indictment (hereafter “Indictment S5” or “S5”), was untimely because it did not relate back to the May 7, 2001 Second Superseding Indictment in which Benussi was initially named, see United States v. Fiore, S2 00 Cr. 1267(LAK) Indictment (hereafter “Indictment S2” or “S2”); and (5) a new trial is required because the general verdict of guilty makes it impossible to determine if the jury relied upon untenable legal theories.
We conclude that none of these claims has merit. We hold that (1) when a member of a conspiracy whose purpose is economic profit knowingly receives a share of the scheme’s anticipated proceeds, whether “actively” by holding out his hand or “passively” by holding out his brokerage account, that conspirator engages in an overt act in furtherance of the conspiracy; (2) the trial evidence in this case sufficed to support a reasonable jury’s finding that Pasciuto did knowingly receive conspiracy proceeds into a brokerage account under his control within the statutory limitations period; (3) because the indictment specifically alleged that the conspiracy extended through the conspirators’ receipt of proceeds, the government’s reliance on un-pleaded overt acts of receipt to satisfy the statute of limitations constituted neither a constructive amendment of the indictment nor an impermissible variance in proof; (4) because Indictment S5 did not materially broaden or substantially amend Indictment S2, it properly related back to the earlier pleading; and (5) no new trial is warranted where, as in this case, any deficiencies in one theory of guilt are factual rather than legal and sufficient evidence supports a guilty verdict on an alternative theory.
*612I. Background
A. The Conspiracy to “Pump and Dump” Securities
On May 7, 2001, Glen Benussi was first charged, together with ten co-defendants, with conspiracy to commit securities fraud, wire fraud, and commercial bribery in connection with the initial public stock offerings of two businesses, Gaylord Companies (“Gaylord”) and Thermo-Mizer Environmental Corporation (“Thermo-Mizer”). See Indictment S2. The conspiracy, a variation on the classic “pump and dump” scheme — whereby persons holding certain securities fraudulently inflate their price (the “pump”) in order to sell at an artificial profit (the “dump”) — is described in detail in Judge Kaplan’s comprehensive opinion denying Benussi’s Rule 33 motion. See United States v. Benussi, 216 F.Supp.2d at 302-07. We assume familiarity with that opinion and here review only the facts necessary to our discussion of the issues on appeal.
In the fall of 1995, Glen Benussi, together with three other principals of Nationwide Securities (“Nationwide”), opened a Manhattan branch office and agreed to underwrite the initial public offering of 750,000 shares of Gaylord common stock. The offering plan provided for stock to be sold at $3.00 per share, with purchasers also offered two warrants per share at a cost of $0.10 each. Each warrant entitled its holder to buy an additional share of Gaylord common stock at the $3.00 offering price during the period between October 31,1996, and October 30, 2000.
Instead of following this plan, Benussi and his confederates secretly agreed to “strip” one warrant from each stock unit. The Nationwide principals divided most of these warrants among themselves, using the remainder to bribe brokers to assist in their scheme to inflate the market price of the Gaylord securities, thereby ensuring significant profits when the conspirators sold their stripped warrants. Meanwhile, the conspirators generally concealed their interests in the stripped warrants by using nominee accounts under their control. For example, Benussi traded stripped warrants in Nationwide accounts in his wife’s maiden name, as well as in the names of two offshore corporations, Barson Holdings, Ltd., and Rum United, Ltd. Louis Pasciuto, a Nationwide broker, traded stripped warrants in Nationwide accounts in the name of his then-girlfriend (subsequently, his wife), Stefanie Feehan.
In February 1996, the conspirators repeated this scheme in connection with the public offering of 750,000 shares of Ther-mo-Mizer common stock. Once again, the offering plan permitted customers to purchase one share of stock, this time at $5.00 per share, together with two warrants at $0.10 each. The conspirators again stripped one warrant from each unit, distributed these stripped warrants among themselves, and fraudulently manipulated the market price of Thermo-Mizer’s securities to inflate the value of their warrants.
B. Sale of the Stripped Warrants
In order not to alert market attention to their scheme, the conspirators agreed not to sell their stripped warrants until trading was approved by Nationwide principal Marco Fiore. In the case of the Gaylord warrants, Fiore’s approval came in mid-November 1995, a short time after the public offering; in the case of the Thermo-Mizer warrants, Fiore authorized sale on February 28,1996, the same day the public offering took effect.
Trading records show that the conspirators did not dispose of their shares in single blocks, but usually employed a series of transactions, often over several months. For example, Benussi used seven *613transactions in two nominee accounts between November 1995 and January 1996, to sell approximately 35,000 Gaylord warrants at prices ranging from $1.00 to $1.75 per warrant. On the other hand, Benussi sold all 190,000 of his Thermo-Mizer warrants on February 28, 1996, the day he acquired them, using four transactions in three nominee accounts, for which he received from $2.50 to $3.38 per warrant. Other conspirators, however, paced their Thermo-Mizer sales over the course of the next few months. Significantly, for purposes of the statute of limitations issue before us, co-conspirator Louis Pasciuto sold approximately 60,000 Thermo-Mizer warrants out of the Stefanie Feehan account through more than a dozen trades executed between May 3, 1996, and June 24,1996.
C. OveH Acts within the Limitations Period
Of the ninety overt acts alleged in Indictment S2, only one involved conduct during the limitations period: “On or about August 9, 1996, [an unindicted co-conspirator] caused a Nationwide customer to sell approximately 850 shares of Ther-mo-Mizer common stock.” Indictment S2 at ¶ 39kkkk. In Indictment S5, the aforementioned overt act was deleted and three other timely overt acts were alleged:
pp. On or about May 7, 1996, Louis Pascuito caused a Nationwide brokerage account in the name of Pascuito’s girlfriend to sell approximately 5,000 Ther-mo-Mizer warrants at approximately $0.38 per warrant.
qq. On or about May 30, 1996, Louis Pascuito caused a Nationwide brokerage account in the name of Pascuito’s girlfriend to sell approximately 4,000 Ther-mo-Mizer warrants at approximately $0.19 per warrant.
rr. On or about June 24, 1996, Louis Pascuito caused a Nationwide brokerage account in the name of Pascuito’s girlfriend to sell approximately 12,010 Ther-mo-Mizer warrants at approximately $0.19 per warrant.
Indictment S5 at ¶ 38pp-rr.
In his Rule 33 motion to the district court, Benussi argued that these unilateral warrant sales could not satisfy the statute of limitations because they evidenced no concerted activity by the conspirators. Indeed, Benussi submitted that the charged conspiracy had ended when the conspirators received their shares of the stripped warrants or, at the latest, in early April 1996, when the conspirators stopped manipulating the Gaylord and Thermo-Mizer securities and Nationwide’s Manhattan office closed. The district court rejected these arguments, holding that the indictment alleged, and the evidence established, that the conspiracy extended through the conspirators’ receipt of profits from sales of the stripped warrants. See United States v. Benussi, 216 F.Supp.2d at 311-14.
In reaching this conclusion, however, the district court identified a different concern with relying on the pleaded overt acts to satisfy the statute of limitations. Specifically, it was unclear to the court whether the trades described in these overt acts actually involved stripped warrants acquired pursuant to the charged conspiracy. Apparently, Pasciuto had sold the majority of his stripped Thermo-Mizer warrants— some 24,750 — in early March 1996, leaving only 2,250 stripped warrants in the Feehan account at the start of May 1996. The other 58,285 Thermo-Mizer warrants in the Feehan account in May 1996 were the product of a fraudulent transfer that Pas-ciuto had made in March 1996 from Benus-si’s Rum United account. These warrants, however, had not been stripped from the initial stock offering; rather, they had been purchased by Pasciuto and certain Nationwide principals on the open market earlier in the month with money appropri*614ated from the Rum United account — initially without Benussi’s knowledge — in an effort to curb the securities’ price decline. As the district court observed,
Even if the ... purchase [of Thermo-Mizer warrants] in the Rum account arguably was in furtherance of the conspiracy, it is not a rational inference that their subsequent theft, transfer, and eventual sale by one or more of the co-conspirators furthered the conspiratorial agreement with which Benussi was charged.
Id. at 314. Nevertheless, the district court concluded that it had not been necessary for the jury to determine exactly which May warrant trades out of the Feehan account involved the 2,250 stripped warrants because trading records plainly showed that the Feehan account received the proceeds for all May sales on or after May 8, 1996.2 Citing this court’s opinion in United States v. Ben Zvi, 242 F.3d 89, 98 (2d Cir.2001), the district court ruled that such “knowing receipt” of conspiracy proceeds satisfied the requirement for an overt act within the limitations period. See United States v. Benussi, 216 F.Supp.2d at 317-19.
II. Discussion
A. A Co-Conspirator’s Knowing Receipt of Conspiracy Proceeds into a Brokerage Account Under His Control Can Constitute an Overt Act in Furtherance of the Charged Scheme
Benussi asserts that receipt of conspiracy proceeds into the Feehan account on or after May 8, 2003, cannot, as a matter of law, bring the charged conspiracy within the statute of limitations.
When a conspiracy requires proof of an overt act, the government satisfies the statute of limitations, see 18 U.S.C. § 3282(a), if it establishes that the conspiracy operated within the five-year period preceding the indictment, and a conspirator knowingly committed at least one overt act in furtherance of the scheme within that period. See Grunewald v. United States, 353 U.S. 391, 396-97, 77 S.Ct. 963, 1 L.Ed.2d 931 (1957); United States v. Ben Zvi, 242 F.3d at 97. Benussi acknowledges this test but asserts that (1) unilateral receipt of proceeds cannot establish an ongoing conspiracy, and (2) passive receipt of proceeds cannot constitute an overt act in furtherance of the scheme. We review these legal claims de novo. See United States v. Coriaty, 300 F.3d 244, 249 (2d Cir.2002).
In evaluating Benussi’s twin challenges, we look to the scope of the charged conspiracy. As the Supreme Court explained in Grunewald v. United States, 353 U.S. at 397, 77 S.Ct. 963, “the crucial question in determining whether the statute of limitations has run is the scope of the conspiratorial agreement, for it is that which determines both the duration of the conspiracy, and whether the act relied on as an overt act may properly be regarded as in furtherance of the conspiracy.”
1. A Conspirator’s Receipt of Anticipated Economic Proceeds Evidences the Continued Operation of a Conspiracy
Benussi argues that the scope of the charged conspiracy extended only to the *615conspirators’ receipt of stripped warrants or, at the latest, to April 8, 1996, when their manipulation of the market for Gay-lord and Thermo-Mizer warrants ended. He insists that the conspiracy alleged in the indictment did not extend to the conspirators’ unilateral sales of their stripped warrants after that April date. See Appellant’s Br. at 32-39. The argument, however, is not supported by the indictments, which specifically allege that the ultimate conspiratorial goal was the sale of fraudulently acquired and inflated securities and the receipt of substantial cash profits. In both Indictments S2 and S5, the grand jury states that defendants
engaged in deceptive and manipulative sales practices in order to sell securities of the Subject IPOs to their retail customers, thus creating demand for, and increasing the price of, the securities, and enabling the defendants to sell the securities they controlled through the nominees at artificially inflated prices. As a result of this scheme, the defendants obtained illegal profits of not less than approximately $2.0 million.
Indictment S2 at ¶ 23; Indictment S5 at ¶ 23.
This court has consistently ruled that where a conspiracy’s purpose is economic enrichment, the jointly undertaken scheme continues through the conspirators’ receipt of “their anticipated economic benefits.” United States v. Mennuti, 679 F.2d 1032, 1035 (2d Cir.1982); accord United States v. LaSpina, 299 F.3d 165, 175 (2d Cir.2002); United States v. Ben Zvi, 242 F.3d at 98; see also United States v. Fletcher, 928 F.2d 495, 500 (2d Cir.1991); United States v. Knuckles, 581 F.2d 305, 313 (2d Cir.1978). This conclusion derives from the well-established principles that (1) a conspiracy continues “until its aim has been achieved, it has been abandoned, or otherwise terminated,” United States v. Rucker, 586 F.2d 899, 906 (2d Cir.1978); and (2) absent withdrawal, a conspirator’s “participation in a conspiracy is presumed to continue until the last overt act by any of the conspirators,” United States v. Diaz, 176 F.3d 52, 98 (2d Cir.1999) (internal quotation marks omitted) (and cases cited therein).
Benussi argues that a conspirator’s receipt of anticipated economic benefits cannot, as a matter of law, prove an ongoing conspiracy if he singularly controls when that receipt occurs; in such a case, there must be some other evidence of concerted activity. His only support for this assertion is an observation in United States v. Roshko, 969 F.2d 1, 8 (2d Cir.1992), that the defendant in United States v. Mennuti had “acted in concert with the other conspirators after the completion of the underlying mail fraud offense in order to further the conspirators’ general criminal objective of securing an economic windfall for themselves.”
In fact, this statement is dictum, intended neither to support the actual holding in Roshko nor to limit the “payoff’ principle articulated in Mennuti. Indeed, Roshko acknowledged that it “makes a good deal of sense” to view “conspiracies for economic gain” as continuing until “ ‘the conspirators receive their anticipated economic benefits’ ” because the receipt of such benefits is the “ ‘sole reason’ ” the conspirators become involved in the scheme. Roshko, 969 F.2d at 8 (quoting United States v. Mennuti, 679 F.2d at 1035). The court simply found the “payoff’ analogy inapt when applied to conspiracies with non-economic goals.
The pleaded purpose of the Roshko conspiracy was procurement of resident alien status for Meir Roshko through a fraudulent marriage, an end achieved outside the statutory limitations period. To avoid dismissal, the prosecution, relying on Mennu-*616ti, argued that the conspiracy extended to Roshko’s subsequent divorce, his remarriage, and his second wife’s adjustment of her immigration status, the last event being Mrs. Roshko’s “payoff’ for her participation in the charged conspiracy. The court disagreed, not, as Benussi suggests, because the conspirators failed to engage in any concerted action during the limitations period, but because their actions within that time frame simply were not in furtherance of the conspiracy’s pleaded purpose. See id. at 8 (“[T]he grand jury did not allege that Irene [Roshko’s] acquisition of permanent resident status was an object of the conspiracy .... Meir’s acquisition of a green card was the object of the conspiracy alleged in this indictment. The subsequent alleged overt acts — his divorce and his marriage to Irene — were superfluous to the success of that object .... ”).
In Benussi’s case, not only was the charged conspiracy economically motivated, the indictment specifically pleaded the receipt of such gain as the ultimate object of the jointly undertaken scheme. See Indictment S2 at ¶ 23; Indictment S5 at ¶ 23 (“As a result of this scheme, the defendants obtained illegal profits of not less than approximately $2.0 million.”). Thus, Roshko, no less than Mennuti, supports the conclusion that the scope of the conspiracy in this case continued through both the conspirators’ sale of the stripped warrants and their receipt of profits.
Benussi’s citation to United States v. Doherty, 867 F.2d 47 (1st Cir.1989), does not alter our conclusion. In that case, although a pleaded objective of the charged conspiracy was the salary increase that would accompany a fraudulently procured police promotion, the First Circuit rejected the government’s argument that each salary payment constituted a new overt act by the defendant. Then-Circuit Judge Breyer, writing for the court, observed that “payoffs” could reasonably be viewed as part of a conspiracy where their receipt “consists of one action, or a handful of actions, taking place over a limited period of time, or where some evidence exists that the special dangers attendant to conspiracies ... remain present until the payoff is received.” Id. at 61. But no such conclusion was warranted “where receiving the payoff merely consists of a lengthy, indefinite series of ordinary, typically noncriminal, unilateral actions, such as receiving salary payments, and there is no evidence that any concerted activity posing the special societal dangers of conspiracy is still taking place.” Id. (emphasis in original).
Were this court to follow Doherty, Be-nussi would not benefit because, in his case, the conspirators’ receipt of profits fits more comfortably into the former Do-herty category than the latter. Although the conspirators’ sales of stripped warrants numbered more than a handful, they were hardly “indefinite” in number or “lengthy” in duration. Indeed, it appears that all the stripped Thermo-Mizer warrants were sold within ten weeks of the public offering and within four weeks of the closing of the Nationwide Manhattan office. This is not surprising. Implicit in the conspiratorial scheme was an understanding that the receipt of benefits depended on selling the stripped warrants before their inflated market price collapsed. Pasciuto’s May 1996 warrant sales out of the Feehan account and his receipt of benefits on and after May 8, 1996, fall within this understanding.
In sum, because a “conspiracy continues so long as overt acts in furtherance of its purposes are done,” United States v. Rucker, 586 F.2d at 906; because receipt of anticipated profits is an overt act in furtherance of an economically-motivated conspiracy, see, e.g., United States v. Ben *617Zvi, 242 F.3d at 98; and because an overt act may be committed by “only a single one of the conspirators,” Braverman v. United States, 317 U.S. 49, 53, 63 S.Ct. 99, 87 L.Ed. 23 (1942); see also United States v. Diaz, 176 F.3d at 98, we reject Benussi’s argument that, as a matter of law, a single conspirator’s receipt of anticipated benefits within the limitations period cannot, by itself, establish an ongoing conspiracy, see generally United States v. LaSpina, 299 F.3d at 174 (holding that where conduct falls within scope of criminal agreement, conspiracy continues “as long as one or more conspirators” engage in such conduct).
2. A Conspirator’s Passive Receipt of Proceeds Can Constitute an Overt Act in Furtherance of the Conspiracy When Stick Receipt is Knowing and Intentional
Citing our statement in Ben Zvi that “[t]o constitute an overt act for purposes of the statute of limitations the act must involve some affirmative conduct or deliberate omission,” United States v. Ben Zvi, 242 F.3d at 97, Benussi submits that the passive receipt of profits into the Feehan account on and after May 8, 1996, cannot, as a matter of law, constitute the affirmative overt act necessary to satisfy the statute of limitations. We disagree.
In Ben Zvi, this court made plain that when the object of a conspiracy is economic profit, defendants engage in the necessary affirmative conduct and, therefore, commit the required overt act when they knowingly take possession of their share of that profit. The Ben Zvi conspirators schemed to defraud their insurer by staging a robbery of their own jewelry store. To determine whether the government satisfied the statute of limitations, the court considered two overt acts. The first charged Luiz Ben Zvi with causing an electronic funds transfer to be made from Lloyd’s of London to Lloyd’s New York attorney. The second charged Ms. Ben Zvi and her brother with causing checks to be drawn from the lawyer’s bank account to pay their insurance claim. The court ruled that the first transfer did not constitute an overt act by Ms. Ben Zvi because “though precipitated by earlier fraudulent acts and omissions of defendant and her coconspirators,” it “did not involve or otherwise turn on any identifiable act or omission of the conspirators as of the time of the wire transfer.” Id. Although the second act similarly involved a financial transfer by an innocent third party precipitated by the defendants, the court identified an important difference: the defendants themselves received the check, which was made payable to their jewelry business. Because this check represented the “anticipated economic benefits” of the conspiracy, the court ruled that its “knowing receipt ... by the defendant and her co-conspirators constituted overt acts in furtherance of the conspiracy.” Id. at 98.3
Benussi submits that Ben Zvi is distinguishable because the conspirators there took physical possession of the anticipated proceeds. But the case does not indicate *618whether the manner of receipt was by the conspirators’ own hands, through a clerical employee, through an attorney or accountant, by direct deposit to the conspirators’ business account, etc. Indeed, the means by which a conspirator takes possession of his share of the scheme’s proceeds is not determinative of his commission of an overt act. A street thief or bank robber may well receive his share of criminal proceeds in hand; a more sophisticated schemer may arrange for fraud proceeds to be wired to his bank or brokerage account — or, as in this case, that of his nominee. In each case, what establishes the receipt as an overt act is not whether the conspirator’s conduct can be labeled “active” or “passive,” but whether the receipt was knowing and intentional. See United States v. Ben Zvi, 242 F.3d at 98 (finding defendants’ “knowing receipt” of conspiratorial proceeds to satisfy overt act requirement). The unwitting receipt of criminal proceeds cannot, after all, constitute an overt act. See United States v. Floyd, 496 F.2d 982, 988 (2d Cir.1974). The requisite knowledge and intent to possess such proceeds, not the means employed to take possession, are the decisive factors in establishing a conspirator’s “affirmative” receipt of the proceeds or, at the least, his “deliberate” failure to renounce them. Ben Zvi, 242 F.3d at 97.
We therefore reject Benussi’s legal challenge and hold that a conspirator’s knowing receipt of criminal proceeds achieved passively through a wire transfer into an account under his control can satisfy the overt act element of conspiracy.
B. Trial Evidence Established Pasciuto’s Knowing Receipt of Conspiracy Proceeds Within the Statute of Limitations
Benussi submits that the trial evidence was insufficient to support a jury finding that Pasciuto knowingly received conspiracy proceeds through the Feehan account on or after May 8, 1996. In assessing a factual sufficiency challenge, we review the evidence in its totality, see United States v. Autuori, 212 F.3d 105, 114 (2d Cir.2000), and in the light most favorable to the prosecution, see United States v. Berger, 224 F.3d 107, 116 (2d Cir.2000), mindful that the task of choosing among permissible competing inferences is for the jury, not a reviewing court, see United States v. Morrison, 153 F.3d 34, 49 (2d Cir.1998). We will affirm the jury’s guilty verdict if “any rational trier of fact could have found the essential elements” of the charged crime “beyond a reasonable doubt.” Jackson v. Virginia, 443 U.S. 307, 319, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979) (emphasis in original); accord United States v. Best, 219 F.3d 192, 200 (2d Cir.2000).
Applying this standard of review, we reach the same conclusion as Judge Kaplan: “there was ample evidence from which the jury reasonably could have concluded that [Pasciuto] knowingly received payments for the sale of warrants in the Feehan account” on and after May 8, 1996. United States v. Benussi 216 F.Supp.2d at 318. Specifically, evidence of Pasciuto’s active participation in the “pump” phase of the conspiracy established his strong motive to “dump” stripped warrants at inflated prices. Trial evidence further revealed that the conspirators almost uniformly used nominee accounts at Nationwide to hold their stripped warrants and to receive profits from the sales thereof. Pasciuto’s wife, Stefanie Feehan, testified that she did not open the Nationwide account in her name out of which thousands of stripped Thermo-Mizer warrants were sold throughout the spring of 1996; rather, Pasciuto advised her that he had opened this account. Ms. Feehan identified Pasciuto’s handwriting on the account’s forged signature cards as well as on a related *619check. She further testified that she had never traded in the account, but when she received proceeds from any transactions therein, she gave them either to Pasciuto or, at his direction, to other persons.
We must assume not only that the jury credited Ms. Feehan’s testimony, but that it drew all reasonable inferences therefrom in the prosecution’s favor. See United States v. Walker, 191 F.3d 326, 333 (2d Cir.1999). Thus, although Ms. Feehan may not have offered direct evidence of Pasciuto’s May sale of Thermo-Mizer warrants from her account or of the subsequent receipt of benefits from those sales, we conclude that the evidence of Pasciuto’s overall control of the account together with his active role in the conspiracy sufficed to support a reasonable jury inference that Pasciuto knowingly received those proceeds and, thereby, committed an overt act in furtherance of the charged conspiracy within the limitations period. See United States v. Ben Zvi, 242 F.3d at 98.
C. Proof of Pasciuto’s Unalleged Overt Acts within the Limitations Period Did Not Constitute a Constructive Amendment of the Indictment or an Impermissible Variance in Proof
Benussi argues that the government cannot satisfy the statute of limitations by proof of an unalleged overt act. Specifically, he submits that the prosecutor’s reliance on Pasciuto’s unalleged receipt of conspiracy proceeds on and after May 8, 1996, violated due process by constructively amending the indictment or, alternatively, by creating a prejudicial variance between the indictment and the proof adduced at trial.
1. Proof of an Unalleged Overt Act Can Satisfy the Statute of Limitations Provided Defendant Has Fair Notice
In United States v. Frank, this court reaffirmed “the well-established rule of this and other circuits that the overt act element of a conspiracy charge may be satisfied by an overt act that is not specified in the indictment, at least so long there is no prejudice to the defendant.” 156 F.3d 332, 337 (2d Cir.1998) (and cases cited therein); accord United States v. LaSpina, 299 F.3d at 182 (“It is clear the Government may offer proof of acts not included within the indictment, as long as they are within the scope of the conspiracy.” (internal quotation marks omitted)). As we explained in United States v. Armone, “[a] principal reason for the overt act requirement in a conspiracy prosecution is simply to manifest that the conspiracy is at work.” 363 F.2d 385, 400 (2d Cir.1966) (internal quotation marks omitted). Thus, as long as defendant is “given notice of the core of criminality to be proven at trial,” this court has afforded the prosecution “significant flexibility” to prove the conspiracy’s operation through both unalleged and alleged overt acts. United States v. Frank, 156 F.3d at 338 (internal quotation marks omitted).
Benussi does not attack this principle as it applies to the general overt act element of conspiracy. Instead, he submits that the principle should not extend to overt acts used to satisfy the statute of limitations. See generally United States v. Davis, 533 F.2d 921, 929 (5th Cir.1976) (holding that conspiracy’s operation within statute of limitations must be proved by an overt act alleged in the indictment). This court expressly rejected an identical argument in United States v. Frank, holding: “We see no reason to devise a special rule for the statute of limitations requirement that is different from the rule governing the overt act element.” 156 F.3d at 339. Benussi urges us to reconsider Frank on the ground that the statute of limitations serves a special purpose — -namely, to pro*620tect against stale prosecutions — which can be met only by requiring proof of a specifically pleaded overt act.
Of course, this panel cannot refuse to follow Frank unless and until its holding is overruled by our court en banc or by the Supreme Court. See Jones v. Coughlin, 45 F.3d 677, 679 (2d Cir.1995). In any event, Benussi’s argument that proof of a pleaded overt act is necessary to serve the staleness concerns of the statute of limitations overlooks the fact that' statutes of limitations presumably serve the same purpose for conspiracies without overt act requirements. See, e.g., United States v. Spero, 331 F.3d 57, 60 (2d Cir.2003) (noting that racketeering conspiracy, see 18 U.S.C. § 1962(d), does not require proof of an overt act); United States v. Grammatikos, 633 F.2d 1013, 1023 (2d Cir.1980) (holding that conspiracies to import or distribute controlled substances, see 21 U.S.C. §§ 846, 963, do not require overt acts to be .pleaded or proved). In such cases, once the government proves the conspiracy’s existence, the scheme’s continued operation into the limitations period is presumed, see United States v. Spero, 331 F.3d at 61, without the jury having to find proved the timely commission of any overt act, alleged or unalleged, see United States v. Grammatikos, 633 F.2d at 1022.
This body of law reinforces Frank’s conclusion that there is no sound reason to devise a special rule for overt acts as they relate to the statute of limitations. “In the matter of the statute of limitations, as in the case of overt acts generally,” the law’s “principal concerns are that a defendant have fair and adequate notice of the charges against him and have suffered no undue prejudice as a result of the proof offered.” United States v. Frank, 156 F.3d at 339. Accordingly, the rule for pleading and proof remains the same: “the statute of limitations may be satisfied by proof of an overt act not explicitly listed in the indictment, as long as a defendant has had fair and adequate notice of the charge for which he is being tried, and he is not unduly prejudiced by the asserted variance in the proof.” Id. We address the question of fair notice in the next section. See id. at 338 n. 5 (observing that issue of whether conspiracy may be proved by an unalleged overt act frequently reduces to the question whether there was a “variance” between the indictment and the proof at trial).
2. Constructive Amendment and Variance
Benussi submits that even if an unal-leged overt act can satisfy the statute of limitations, in his case the government im-permissibly “amended and varied the indictment by relying on evidence that the charged conspiracy continued by virtue of [Pasciutoj’s sale of non-stolen Thermo-Mizer warrants whereas the [Indictment S5] referred only to the sale of stolen Thermo-Mizer warrants.” Appellant’s Br. at 55.
a. Constructive Amendment
“To prevail on a constructive amendment claim, a defendant must demonstrate that either the proof at trial or the trial court’s jury instructions so altered an essential element of the charge that, upon review, it is uncertain whether the defendant was convicted of conduct that was the subject of the grand jury’s indictment.” United States v. Frank, 156 F.3d at 337; see also United States v. Wallace, 59 F.3d 333, 337 (2d Cir.1995). “Where charges are constructively narrowed or where a generally framed indictment encompasses the specific legal theory or evidence used at trial,” there is no constructive amendment. United States v. Wallace, 59 F.3d at 337 (internal quotation *621marks omitted); cf. Stirone v. United States, 361 U.S. 212, 218, 80 S.Ct. 270, 4 L.Ed.2d 252 (1960) (noting that indictment written in general terms may support conviction on alternative bases). In short, not all modifications constitute constructive amendments. In this case, the limitations element of the charged conspiracy required the prosecution to prove a timely overt act. But, as already discussed, the prosecution could carry its burden on this element by proving any alleged or unal-leged overt act that fit within the “core of criminality” identified in the indictment. United States v. Frank, 156 F.3d at 338; see also United States v. Patino, 962 F.2d 263, 266 (2d Cir.1992) (citing approvingly United States v. Robison, 904 F.2d 365, 369 (6th Cir.1990)) (upholding 18 U.S.C. § 924(c) conviction where indictment charged use of a .357 Magnum but proof showed use of a shotgun, because the specific type of firearm used by the conspirator was not an essential element of the crime).
The core criminality pleaded in this indictment was a fraud scheme, operating between October 1995 and June 1996, whose ultimate purpose was the conspirators’ realization of millions of dollars in illegal profits from them sales of inflated stripped warrants. See Indictment S5 at ¶¶ 23, 24. Indictment S5 identified twenty-five occasions on which conspirators, including Pasciuto, engaged in the sale of such warrants. Id. at ¶ 38. Under these circumstances, proof of other unalleged sales of stripped warrants during the conspiratorial period hardly constitutes a constructive amendment of the pleadings.
Contrary to the argument advanced on appeal by Benussi, nowhere did the indictment allege that warrant sales within the limitations period involved only stolen, as opposed to stripped, securities. Rather, as the district court noted, the proof at trial raised a question as to which May sales involved stripped warrants and which sales involved stolen warrants. But the fact that the prosecution might have proved certain alleged overt acts that may not have furthered the charged conspiracy did not preclude it from proving other unal-leged overt acts falling squarely within the charged scheme. In sum, although Pasci-uto’s sales of stripped warrants in early May 1996 and his receipt of proceeds therefrom on or after May 8, 1996, were not specifically pleaded in the indictment, they are plainly within the charged core of criminality and constitute a permissible alternative basis for proving the general allegation that the conspiracy continued for several weeks into the limitations period.
b. Variance
“A variance occurs when the charging terms of the indictment are left unaltered, but the evidence offered at trial proves facts materially different from those alleged in the indictment.” United States v. Frank, 156 F.3d at 337 n. 5 (internal quotation marks and emphasis omitted). Although the distinction between constructive amendment and variance may appear “merely one of degree,” there is an important difference in outcome: “a constructive amendment of the indictment is considered to be a per se violation of the grand jury clause, while a defendant must show prejudice in order to prevail on a variance claim.” Id.; see also United States v. McDermott, 245 F.3d 133, 139 (2d Cir.2001) (reiterating principle that variance must cause “substantial prejudice” to warrant reversal).
A defendant cannot demonstrate that he has been prejudiced by a variance where the pleading and the proof “substantially correspond, where the variance is not of a character that could have misled the defendant at the trial, and *622where the variance is not such as to deprive the accused of his right to be protected against another prosecution for the same offense.” United States v. Mucciante, 21 F.3d 1228, 1236 (2d Cir.1994) (internal quotation marks omitted). In this case, because Indictment S5 gave Benussi fair and adequate notice that the conspiratorial scheme achieved its ultimate economic purpose through the conspirators’ multiple sales of stripped securities and their receipt of proceeds through June 1996, Benussi cannot show that he was prejudiced by proof of a few uncharged proceed receipts after May 8, 1996.
D. Indictment S5 Relates Back to Indictment S2 for Purposes of Calculating the Statute of Limitations
Benussi submits that Indictment S5, filed on August 8, 2001, more than five years after the last overt act in furtherance of the charged conspiracy, should have been dismissed as untimely. He asserts that Indictment S5 does not relate back to the timely filed Indictment S2 because the two pleadings allege different time frames for the charged conspiracy and different overt acts within the limitations period. We review this question of law de novo. See United States v. Yousef, 327 F.3d 56, 137 (2d Cir.2003).
“It is black letter law that ‘[o]nce an indictment is brought, the statute of limitations is tolled as to the charges contained in that indictment.’ ” United States v. Ben Zvi, 242 F.3d at 98 (quoting United States v. Grady, 544 F.2d 598, 601 (2d Cir.1976)); accord United States v. Gengo, 808 F.2d 1, 3 (2d Cir.1986). Further, a superseding indictment that supplants a pending timely indictment relates back to the original pleading and inherits its timeliness as long as the later indictment does not materially broaden or substantially amend the original charges. See Gengo, 808 F.2d at 3. In determining whether a superseding indictment materially broadens or amends the original charges, we will consider whether the additional pleadings allege violations of a different statute, contain different elements, rely on different evidence, or expose the defendant to a potentially greater sentence. See United States v. Ben Zvi, 168 F.3d 49, 55 (2d Cir.1999). No single factor is determinative; rather, the “touchstone” of our analysis is notice, i.e., whether the original indictment fairly alerted the defendant to the subsequent charges against him and the time period at issue. See United States v. Gengo, 808 F.2d at 3, cf. United States v. Ben Zvi, 168 F.3d at 55 (holding that notice must come in indictment).
To the extent Indictment S5 alleges a different time frame for the conspiracy (October 1995 through June 1996) than Indictment S2 (October 1995 through August 1996), the law is clear that there is no obstacle to relation back when a superseding pleading narrows, rather than broadens, the original charges. See United States v. Ben Zvi, 168 F.3d at 54; United States v. Grady, 544 F.2d at 602. Accordingly, we reject this part of Benussi’s challenge without further discussion.
This court has not yet ruled on whether the addition of new overt acts to a superseding indictment constitutes a substantial alteration in the original charge so as to preclude relation back. Cf. United States v. Gengo, 808 F.2d at 3 (noting that the issue, although raised in the district court, was not pursued on appeal because the overt acts in question had been dismissed on other grounds). A number of our sister circuits have upheld relation back where additional overt acts simply flesh out or provide more detail about the originally charged crime without materially broadening or amending it. See, e.g., *623United States v. Pearson, 340 F.3d 459, 465 (7th Cir.2003) (holding that addition of three overt acts of concealment in superseding indictment did not preclude relation back because “the uninterrupted success of the conspiracy turned on defendants’ ability to continuously conceal the truth about the defective batteries from consumers and ... shareholders”); United States v. Lash, 937 F.2d 1077, 1081-82 (6th Cir.1991) (holding that although additional overt acts in superseding indictment supplied “different details” about the operation of the conspiracy, both indictments “described the same conspiracy to defraud investors during the same time frame through the operations” of the same two businesses); see also United States v. O’Bryant, 998 F.2d 21, 24-25 (1st Cir.1993) (holding that superseding indictment containing “more detail in terms of overt acts” than original pleading, nevertheless related back because “the initial indictment informed appellant in no uncertain terms that he would have to account for essentially the same conduct with which he was ultimately charged in the superseding indictment”). We adopt this approach and hold that the same standard of review applies to overt acts as to any other aspect of a superseding pleading, i.e., whether the new acts materially broaden or substantially amend the original pleading. See United States v. Ben Zvi, 242 F.3d at 98.
Applying that standard to this case, we conclude that the overt acts added in Indictment S5 — all relating to Pasciuto’s sale of warrants out of the Feehan account in May and June 1996 — did not materially broaden or substantially amend the conspiracy charged in Indictment S2. Both S2 and S5 alleged the identical economically motivated conspiracy to commit fraud and bribery in order to strip warrants from Gaylord and Thermo-Mizer stock offerings, to inflate the price of those securities, and then to sell the stripped warrants at the inflated price, thereby netting millions of dollars in fraudulent profits for the conspirators. See Indictment S2 at ¶¶ 22, 23; Indictment S5 at ¶¶ 22, 23. S2 served clear notice on Benussi that the prosecution intended to prove numerous sales of stripped warrants by various conspirators as overt acts in furtherance of the charged scheme. Indeed, thirty-six such sales were pleaded in S2. See Indictment S2 at ¶ 39r, s, t, u, w, x, z, aa, cc, dd, ff, gg, ii, jj, kk, mm, nn, oo, pp, qq, tt, w, xx, zz, bbb, ddd, fff, hhh, iii, 111, qqq, cccc, dddd, eeee, gggg, iiii. Although the last of these sales occurred in March 1996, S2 charged the conspiracy’s continuance through August 1996. Thus, Benussi cannot establish either unfair surprise or prejudice from the superseding indictment’s identification of an additional three warrant sales in May and June 1996.
To the extent Benussi attempts to analogize his case to United States v. Ratcliff, 245 F.3d 1246, 1253-54 (11th Cir.2001), in which relation back was denied because a superseding indictment expanded the original conspiracy by a dozen years, seven additional smuggling ventures, and ten additional co-conspirators, the factual comparison is obviously inapt. Like the defendants in O Bryant, Pearson, and Lash, Benussi was informed by Indictment S2 “in no uncertain terms that he would have to account for essentially the same conduct with which he was ultimately charged” in Indictment S5, United States v. O'Bryant, 998 F.2d at 24, i.e., a scheme to “pump and dump” Gaylord and Thermo-Mizer securities. The three additional overt acts provided a bit more detail about one co-conspirator’s sale of Thermo-Mizer warrants at an inflated profit, but Benussi had certainly been given ample notice in the original pleading that there were numerous such sales and that each one furthered the conspiracy. In sum, the additional overt *624acts did not broaden or substantially amend the original charge in this case; accordingly, Indictment S5 was properly deemed timely as related back to Indictment S2.
E. The General Verdict in this Case Does Not Require a New Trial
As an alternative to reversal, Benussi seeks a new trial on the ground that it is impossible to determine whether the jury’s general verdict of guilty was based upon (1) the securities fraud objective of the conspiracy to which Pasciuto’s timely receipt of proceeds related, or the wire fraud or bribery objectives, for which there was no timely overt act; and (2) Pasciuto’s timely receipt of profits from the sale of stripped or stolen warrants. See Yates v. United States, 354 U.S. 298, 312, 77 S.Ct. 1064, 1 L.Ed.2d 1356 (1957), overruled on other grounds, Burks v. United States, 437 U.S. 1, 10, 98 S.Ct. 2141, 57 L.Ed.2d 1 (1978). The argument is both legally and factually unconvincing.
In Yates v. United States, the Supreme Court considered a general guilty verdict on a Smith Act conspiracy with the twin objects of (1) advocating the overthrow of the United States government and (2) organizing, as the Communist Party of America, a society of persons to so advocate. The Court ruled that because the law’s organization prohibition referred only to the creation of the Communist Party — an event indisputably occurring outside the applicable statute of limitations — the conspiracy conviction could not rest on that objective. Id. at 304-11, 77 S.Ct. 1064. Rejecting the government’s argument that the conviction could be affirmed on the advocacy objective, the Court stated that a general verdict must be set aside where it “is supportable on one ground, but not on another, and it is impossible to tell which ground the jury selected.” Id. at 312, 77 S.Ct. 1064.
In Griffin v. United States, 502 U.S. 46, 56-59, 112 S.Ct. 466, 116 L.Ed.2d 371 (1991), however, the Court clarified that Yates’s broad pronouncement applies only when there is legal error in one of the bases for conviction. The Court explained that by “legal error,” it meant “a mistake about the law,” not “a mistake concerning the weight or the factual import of the evidence.” Id. Indeed, where the error in a verdict is factual, as where one basis for conviction is “unsupported by sufficient evidence,” a guilty verdict “ ‘stands if the evidence is sufficient with respect to any one of the acts charged.’ ” Id. at 56-57, 112 S.Ct. 466 (quoting Turner v. United States, 396 U.S. 398, 420, 90 S.Ct. 642, 24 L.Ed.2d 610 (1970)).
The errors of which Benussi complains are not “legal” in the sense identified in Griffin. Indeed, with respect to the three criminal objectives of the charged conspiracy — securities fraud, wire fraud, and bribery — Benussi fails to establish even a factual error. As we have repeatedly noted in this opinion, the indictments consistently identify profit as the conspirators’ ultimate goal in pursuing the triple criminal objectives of their scheme, specifically, the $2 million in profit eventually realized from the conspirators’ sale of inflated securities. Thus, the jury could reasonably have found that Pasciuto’s receipt of profits on and after May 8, 1996, was a timely overt act in furtherance of any of the three conspiratorial objectives. See generally United States v. Mennuti, 679 F.2d at 1035; accord United States v. LaSpina, 299 F.3d at 175; United States v. Ben Zvi, 242 F.3d at 98; United States v. Fletcher, 928 F.2d at 500; United States v. Knuckles, 581 F.2d at 313. In any event, because the issue of whether Pasciuto’s knowing receipt of profits from the *625sale of stripped warrants was “in furtherance” of any of the conspiracy’s stated objectives was a fact question for the jury, see United States v. Diaz, 176 F.3d at 99, any error in ascribing the acts to a single objective would not require the guilty verdict to be set aside because, as Benussi concedes, Pasciuto’s acts could certainly be found to be in furtherance of the conspiracy’s securities fraud objective, see Griffin v. United States, 502 U.S. at 56-57, 112 S.Ct. 466.
The same conclusion pertains to Benus-si’s argument that the jury may have erroneously based its verdict upon Pasciuto’s receipt of proceeds from the sale of stolen rather than stripped warrants. There is no question that the proceeds at issue— whether from the sale of stolen or stripped warrants — were received into the Feehan account within the limitations period. Thus, this case presents no “legal error” akin to that in Yates. Instead, as Judge Kaplan explained, the problem with reliance on Pasciuto’s May sale of stolen warrants was one of factual insufficiency: the prosecution had failed to adduce evidence to support a reasonable jury inference that the sale of stolen warrants was in furtherance of the charged conspiracy. See United States v. Benussi, 216 F.Supp.2d at 314, 325; see generally Grunewald v. United States, 353 U.S. at 410-11, 77 S.Ct. 963. But because the evidence was sufficient to support a reasonable jury finding that Pas-ciuto’s timely receipt of proceeds from the sale of stripped warrants was in furtherance of the charged scheme, no new trial is required. See Griffin v. United States, 502 U.S. at 56-57, 112 S.Ct. 466.
III. Conclusion
For the reasons stated, we conclude that (1) a conspirator’s knowing, albeit passive, receipt of scheme proceeds into a brokerage account under his control can constitute an overt act in furtherance of the conspiracy; (2) the trial evidence in this case sufficed to establish a co-conspirator’s knowing receipt of conspiracy proceeds within the statutory limitations period; (3) an unalleged overt act can satisfy the statute of limitations element of conspiracy, where, as in this case, the act constitutes neither a constructive amendment of the indictment nor an impermissible variance in proof; (4) the addition of new overt acts to Indictment S5 did not materially broaden or significantly amend the charges originally filed in Indictment S2 so as to preclude relation back; and (5) no new trial is required by factual insufficiencies in certain prosecution theories because the jury’s general verdict of guilty was supported by sufficient proof on alternative theories. Accordingly, Benussi’s judgment of conviction is hereby Affirmed.
. Although Mr. Pasciuto’s name is alternatively spelled "Pasciuto” and "Pascuito” in the record before this court, in this opinion we adopt the spelling used by both sides in their appellate briefs, except in direct quotations of documents in the record.
. On appeal, Benussi points to government trial exhibits suggesting that the Thermo-Mizer warrants traded out of the Feehan account on or after May 7, 1996, were those bought on the open market and stolen from Benussi. Thus, he asserts, the stripped warrants derived from the conspiracy had to have been among those traded earlier, between May 3 and May 6, 1996. See Gov't Ex. 407-C. The government does not contend otherwise, but urges us to focus, as the district court did, on the dates the Feehan account received proceeds from all May warrant sales.
. The prosecution cites Ben Zvi to support its argument that "it is of no legal significance that the overt act that occurred within the limitations period was not actually performed by Benussi, Pasciuto, or any other member of the charged conspiracy.” Appellee's Br. at 26. We emphasize that Ben Zvi does not alter the requirement that an overt act must be knowingly committed by at least one member of a conspiracy. See 18 U.S.C. § 371; see also Braverman v. United States, 317 U.S. at 53, 63 S.Ct. 99; United States v. Floyd, 496 F.2d 982, 988 (2d Cir.1974). Indeed, it was precisely because the Ben Zvi conspirators' knowing receipt of proceeds was their act— separate and distinct from the lawyer's drawing of the check — that the court held that the overt act requirement was satisfied.