Kathy McKenna appeals the district court’s orders granting a preliminary injunction against transfer of disputed stock in PPR Realty, Inc., and its affiliated companies (collectively, “PPR”), and denying her motion to dissolve the injunction. We conclude that the district court did not abuse its discretion by entering the injunction, and that the district court correctly concluded that it lacked jurisdiction to dissolve the injunction while an appeal of the order granting the injunction was pending.
I
PPR is a closely held real estate brokerage and related services concern with multiple offices in and around Pittsburgh, Pennsylvania. PPR is a franchisee of Prudential Real Estate Affiliates, Inc. (“PREA”), a national franchisor of real estate brokerages. In late September 1995, Kathy McKenna, a PPR employee who had acquired 10% of PPR Realty and 5% of its affiliated companies, offered to purchase for $460,000 the shares of Herman and Howard Engelberg, who together held nearly 40% of PPR’s shares. The Engelbergs notified the managing shareholders, Ron Croushore and Helen Sosso, of McKenna’s offer to purchase the stock, and communicated their acceptance of McKenna’s offer to her.
Sosso and Croushore each responded to the notice by asserting that, under a 1990 “Pre-Incorporation Agreement” and subsequent amendments (collectively, “the Shareholder Agreement”), they possessed rights of first refusal to purchase the En-gelbergs’ shares. On a promise of indemnity should McKenna sue, the Engelbergs offered Sosso and Croushore their shares.
The Shareholder Agreement subjected share transfers to the terms of “any then effective franchise agreement entered into by [PPR].” PPR’s Franchise Agreement with PREA granted PREA rights of first *871refusal and consent to any transfers of more than 25% of the equity in the franchised companies. The Franchise Agreement required PREA to exercise its rights within ten days of receiving notice concerning a proposed transfer, and provided for renewed rights should the transfer not be effected within 90 days, or upon a material change in terms of the proposed transfer.
PPR notified PREA of the proposed transfer to Sosso and Croushore. PREA responded that it declined to exercise its right of first refusal, and consented to the transfer of stock from the Engelbergs to Sosso and Croushore. Shortly after the transfer took place, McKenna initiated an arbitration against Croushore, Sosso, the Engelbergs, and PPR. McKenna claimed that she, and not Croushore and Sosso, had the right to buy the Engelbergs’ stock under the Shareholder Agreement.
The arbitrators’ March 1998 award declared that “Kathy McKenna ... should have been offered the shares of Howard Engelberg and Herman Engelberg prior to the Managing Shareholders....” The arbitrators awarded McKenna “specific performance of the Agreement between the parties set forth in the exchange of letters between Kathy McKenna and the Engelbergs of September 28, 1995 and October 3, 1995 ...,” and directed the arbitration defendants “to implement such specific performance.”
McKenna petitioned the Pennsylvania Court of Common Pleas to enforce the award, while Sosso and Croushore petitioned to vacate it. On March 9, 1998, Sosso and Croushore sent copies of the award and their petition to vacate to PREA. On March 31, PREA sent a letter to McKenna stating its understanding that the arbitration had been decided and had been appealed. PREA’s letter asserted that under the Franchise Agreement, the transfer would require PREA’s consent should the award survive appeal. In the interim, PREA requested that McKenna complete certain forms and meet with PREA’s representatives for the purpose of assessing her qualifications.
In response to the opposing petitions, the Pennsylvania court sent the parties back to the arbitration panel to resolve various outstanding issues, including whether McKenna had failed to meet certain “conditions precedent” to receiving the shares under the Franchise Agreement. On August 28, 1998, the arbitrators entered a second award reaffirming the first, and setting out detailed terms for the transfer. The award ordered transfer of the stock
[o]n payment to Helen Sosso and Ron Croushore the amount due by Kathy McKenna of $450,000 and ($10,000 to Herman and Howard Engelberg) and the payment of $95,830 to Helen Sosso and Ron Croushore ..., net of the amount of distributions and dividends Kathy McKenna should have received as a shareholder and interest....
Respecting the effect of the Franchise Agreement, the award continued:
Nothing in this Award is meant to override the requirements and obligations set forth in the Franchise Agreement ..., but the arbitrators deny PPR’s claim that there has been a failure by Kathy McKenna of a condition precedent under the Agreement with PREA; and PPR is ordered to submit to PREA a request to approve the transfer of ownership interest in PPR to Kathy McKenna.
In addition, the award enjoined Sosso, Croushore, and PPR from “doing any act that would materially adversely affect Kathy McKenna’s full right to ownership as provided in this order....”
On September 1, 1998, McKenna notified Sosso and Croushore of her willingness to tender the net price due for the stock under the award, which she calculated to be $66,425 as of that date. On September 4, Sosso and Croushore sent a copy of the award to PREA under cover of a letter, on PPR letterhead, notifying *872PREA of the proposed transfer to McKen-na, and offering to sell PREA the stock for the same price pursuant to PREA’s right of first refusal under the Franchise Agreement.
On September 14, 1998, over McKenna’s objection, PREA responded that it intended to exercise its right to purchase the stock on the terms available to McKenna under the award. PREA then filed this suit in federal court in the Central District of California, naming McKenna, Sosso, Croushore, and PPR as defendants, and seeking a declaration that PREA is entitled to purchase the shares. At the same time, McKenna petitioned the Pennsylvania court to confirm the arbitration award.
In November 1998 the Pennsylvania court entered a nonfinal order granting McKenna’s petition to confirm the award. In February 1999 the Pennsylvania court entered its final order enforcing the award. The final enforcement order substantially repeated the terms of the arbitration award, except that the paragraph concerning PREA’s rights under the Franchise Agreement was shortened to a single sentence: “PPR is ordered to submit to PREA a request to approve the transfer of ownership interest in PPR to Kathy McKenna.” A second order the same day denied McKenna’s motion to hold her adversaries in contempt of the Pennsylvania court’s November order confirming the award. The order enforcing the arbitration award was affirmed by the Pennsylvania Superior Court shortly before this case was argued, and at the time of argument was pending review before the Pennsylvania Supreme Court.
Meanwhile, in January 1999, the California district court issued a preliminary injunction prohibiting McKenna, Sosso, Croushore, and PPR from transferring the stock. McKenna appealed the preliminary injunction, and then moved the district court to dissolve it on the ground that a declaration offered in support of the injunction had contained false statements regarding the intention of the Pennsylvania judge to defer to the California proceedings. On the ground that McKenna’s appeal of the preliminary injunction order divested the district court of jurisdiction to dissolve the injunction, the district court denied the motion to dissolve the injunction. McKenna’s appeal of the order denying her motion to dissolve the injunction was consolidated with her appeal of the injunction itself.
II
McKenna argues (1) that the district court lacks subject matter jurisdiction because the parties were improperly aligned, (2) that the injunction was improper on the merits, (3) that the injunction is barred by the Anti-Injunction Act, and (4) that the district court erroneously concluded that it lacked jurisdiction to consider her motion to dissolve the injunction.
HI
The district court’s jurisdiction and our jurisdiction on appeal are based on diversity of citizenship. See 28 U.S.C. § 1332 (1994). The plaintiff PREA is a California corporation with its principal place of business in California, and the defendants are each individual or corporate citizens of Pennsylvania. McKenna urges that Sosso, Croushore, and PPR should be realigned according to their interests in this lawsuit as plaintiffs with PREA. The realignment of any defendant as a plaintiff would place Pennsylvania citizens on both sides of this case, and divest the federal courts of jurisdiction.
A
The issue of alignment for purposes of diversity jurisdiction requires a court to “look beyond the pleadings” to the actual interests of the parties respecting the subject matter of the lawsuit. City of Indianapolis v. Chase Nat’l Bank, 314 U.S. 63, 69, 62 S.Ct. 15, 86 L.Ed. 47 (1941) (quotations omitted). This inquiry involves factual determinations of the type *873ordinarily left to the district court and reviewed for clear error. See United States ex rel. Aflatooni v. Kitsap Physicians Servs., 163 F.3d 616, 521 (9th Cir. 1999) (as amended). McKenna did not challenge jurisdiction in the district court before taking this appeal, and the district court has entered no findings of fact concerning the actual alignment of interests among the parties. Nevertheless, we are obliged to confront the question of jurisdiction whenever it is apparent that proper alignment of the parties might destroy complete diversity of citizenship. See Continental Airlines, Inc. v. Goodyear Tire & Rubber Co., 819 F.2d 1519, 1522-23 (9th Cir.1987).
B
We must align for jurisdictional purposes those parties whose interests coincide respecting the “primary matter in dispute.” Continental Airlines, 819 F.2d at 1523; see Chase, 314 U.S. at 69, 62 S.Ct. 15; Dolch v. United Cal. Bank, 702 F.2d 178, 181 (9th Cir.1983). The primary matter in dispute here is whether the Franchise Agreement grants PREA a right of first refusal to purchase the Engelbergs’ stock on the terms available to McKenna under the Pennsylvania arbitration award. Regardless of who prevails on this question, Sosso and Croushore, with PPR’s cooperation, must transfer the stock. The only question posed here is to whom. Respecting this question, the interests of Sos-so, Croushore, and PPR are essentially those of constructive trustees with no stake in the outcome except to be released of them charge.
We will ignore the citizenship of “nominal or formal parties who have no interest in the action,” and are “ ‘merely joined to perform the ministerial act of conveying the title if adjudged to the complainant.’ ” 13B Charles Alan Wright, Arthur R. Miller, Edward H. Cooper, Federal Practice and Procedure § 3606, at 409 & n. 2 (2d ed.1984) (quoting Walden v. Skinner, 101 U.S. 577, 588-89, 25 L.Ed. 963 (1879)); see Matchett v. Wold, 818 F.2d 574, 576 (7th Cir.1987) (“The addition to a lawsuit of a purely nominal party-the holder of the stakes of the dispute between the plaintiff and the original defendant-does not affect diversity jurisdiction.”); cf. Dolch, 702 F.2d at 181 (a party’s status as trustee does not control alignment). Inasmuch as Sosso, Croushore, and PPR are joined as defendants in this suit in their capacities as mere stakeholders, we need not realign them as plaintiffs for purposes of determining jurisdiction.
C
We must nevertheless realign a stakeholder that also possesses and pursues its own interests respecting the primary issue in a lawsuit. In Dolch, for example, we realigned a party who was named as a defendant in her capacity as a trustee, but who stood to benefit personally should the plaintiff prevail, and who had admitted every allegation in the complaint and pursued only her personal interests in the litigation. See id. Similarly, Sosso, Croushore, and PPR have admitted every material allegation in PREA’s complaint, and have joined PREA at every step in seeking and defending a preliminary injunction against transfer of the disputed shares.
It is clear that Sosso, Croushore, and PPR are interested in maintaining the injunction in this suit prohibiting transfer of the stock while their appeal is resolved in Pennsylvania state court. This interest explains their concerted action with PREA in obtaining and defending the federal injunction. But it does not establish an alignment of interest with PREA respecting the ultimate issue in this case. PREA’s ultimate claim is that it is entitled to purchase the stock on the same terms available to McKenna under the arbitration award. This claim assumes that the arbitration award will ultimately become final on appeal in Pennsylvania state court. In that case, the interests of Sosso, Crou-*874shore, and PPR in this suit will be those of mere stakeholders charged with delivering the stock to the prevailing party. Should the Pennsylvania Supreme Court overturn the award, Sosso and Croushore will retain ownership of the stock under the 1995 transfer to which PREA consented. This would defeat PREA’s claim in this suit that it is entitled to purchase the stock.
Respecting the ultimate right to purchase the stock that is the primary matter in dispute in this case, Sosso, Croushore, and PPR are either disinterested, or have interests antagonistic to PREA, depending on the outcome of the Pennsylvania appeal. Their alignment with PREA in securing and maintaining the preliminary injunction relates only to the subsidiary issue of whether PREA is entitled to maintain the status quo ante pending resolution of the ultimate dispute, and not to the ultimate dispute itself.
D
That Sosso and Croushore might prefer PREA over McKenna as a prospective business partner does not create an interest concerning the primary issue in this suit that warrants realignment. Where we have realigned parties according to their interests, those interests have involved substantial legal rights or detriments flowing from the resolution of the primary matter in. dispute. In Continental, we aligned an escape-slide supplier with an aircraft manufacturer when the supplier stood to avoid liability for an air disaster if the manufacturer prevailed in the suit. See 819 F.2d at 1523. In Dolch, the realigned trustee stood to gain a beneficial interest in the trust if the plaintiff prevailed. See 702 F.2d at 181. No similar legal benefits or detriments to Sosso, Croushore, or PPR hinge on the outcome of this suit. Though Sosso and Croushore appear to disfavor McKenna, their mere preference regarding an outcome in which they have no legal stake is insufficient to compel realignment.
We decline to realign the parties for purposes of determining the existence of diversity jurisdiction, and proceed to consider the merits of the appeals.
IV
A district court’s grant of a preliminary injunction is subject only to “limited review,” and will be reversed “only if the district court abused its discretion by basing its decision on an erroneous legal standard or on clearly erroneous factual findings.” FTC v. Affordable Media, LLC, 179 F.3d 1228, 1233 (9th Cir.1999) (quotations omitted).
In this circuit, preliminary injunctive relief is available to a party who demonstrates either (1) a combination of probable success and the possibility of irreparable harm, or (2) that serious questions are raised and the balance of hardship tips in its favor. These two formulations represent two points on a sliding scale in which the required degree of irreparable harm increases as the probability of success decreases.
Arcamuzi v. Continental Air Lines, Inc., 819 F.2d 935, 937 (9th Cir.1987) (citations and quotations omitted).
A
The district court found that PREA possessed a right of first refusal under the Franchise Agreement respecting the proposed transfer of shares to McKenna under the arbitration award. On this basis, the district court concluded that PREA was likely to succeed on the merits.
1
The Franchise Agreement provides that it and “the totality of the legal relations of the parties [tjhereto shall be governed by” California law, “except that statutes or regulations of that state pertaining to the franchise relationship” shall apply only to franchisees operating or domiciled in California. The franchisee in this case operates and is domiciled in Pennsylvania, and *875we therefore apply California decisional law, but not California statutory franchise law, to the question of how or whether PREA’s right of first refusal under the Franchise Agreement should be enforced.
2
McKenna argues that contractual provisions giving outsiders rights of first refusal to purchase interests in closely-held corporations are disfavored, and rarely enforced. No California case addresses whether a provision in a franchise agreement may reserve a right of first refusal in a franchisor to purchase the shares of a closely held franchisee. In the absence of California authority on point, “we must use our own best judgment in predicting” how the California Supreme Court would resolve this question. State Farm Mutual Auto. Ins. Co. v. Davis, 937 F.2d 1415, 1418 (9th Cir.1991).
In another context, the California courts have held that corporate bylaws granting rights of first refusal to other shareholders or to the corporation are ordinarily enforceable. See Tu-Vu Drive-In Corp. v. Ashkins, 61 Cal.2d 283, 38 Cal.Rptr. 348, 391 P.2d 828, 830 (1964); Yeng Sue Chow v. Levi Strauss & Co., 49 Cal.App.3d 315, 317, 122 Cal.Rptr. 816 (1975). Rights of first refusal favoring other shareholders or the corporation are reasonable because they
are frequently essential to a successful enterprise; they perform an important function in precluding unwanted intrusions by outsiders; they preserve the integrity of the functioning entity. Such bylaws are necessary for the protection of the corporation and its stockholders against rivals in business or others who might purchase its shares for the purpose of acquiring information which might thereafter be used against the interests of the company.
Tu-Vu, 38 Cal.Rptr. 348, 391 P.2d at 830 (quotations omitted).
Similar concerns to those expressed by the California Supreme Court in Tu-Vu favor the enforcement of a provision reserving a right of first refusal in a franchisor respecting transfers of a substantial interest in a franchisee. A franchisor’s stock in trade is its good name and its business model. These are vulnerable not only to intrusion by outsiders, but also, as may be the case here, to insurgenee by insiders whose acquisition of a larger stake may alter the management or control of the franchisee. A franchisor’s right of first refusal reasonably addresses this eventuality.
The expectation that California courts will ordinarily enforce a franchisor’s right of first refusal to purchase an interest in a franchisee is evident in caveats to California statutes that might otherwise restrict such rights. See Cal. Bus. and Prof.Code § 20025 (no restriction on nonrenewal “shall prohibit a franchisor from exercising a right of first refusal to purchase the franchisee’s business”); id. § 20027 (no provision respecting rights of franchisee’s survivors “shall prohibit a franchisor from exercising the right of first refusal to purchase a franchise”); cf. Cal. Vehicle Code § 11713.3 (limiting franchisor’s exercise of first refusal rights to purchase interests in certain kinds of licensed businesses). Though California statutory franchise law does not govern the franchise relationship in this case, it is instructive that the California legislature in these instances plainly saw itself as preserving, and not creating, the ability of franchisors to enforce first refusal rights. ■ Though not controlling, such pronouncements are at least persuasive authority that the California Supreme Court, if confronted with this issue, would uphold a franchisor’s right of first refusal.
We conclude that the California Supreme Court would enforce an otherwise valid provision in a franchise agreement granting a franchisor a right of first refusal respecting a proposed transfer of shares in its franchisee.
3
The record indicates that, on October 15, 1993, McKenna signed a shareholder *876agreement titled “Fourth Amendment to Pre-Incorporation Agreement.” The Fourth Amendment states that the parties agreed to be bound by the earlier Pre-Incorporation Agreement, which was incorporated by reference and attached as an exhibit. The Pre-Incorporation Agreement, dated March 1st, 1990, states that “[a]ny transfer of Shares will be subject to ... any then effective franchise agreement entered into by the Corporation.” The Second Amendment to the Pre-Incorpo-ration Agreement, dated February 7, 1991, also incorporates by reference “[t]he terms, covenants, and conditions of any franchise agreement.” All of this supports the district court’s conclusion that “McKenna agreed to be bound by the terms ... of any franchise agreement entered into by PPR.”
The original Franchise Agreement between PPR and PREA is dated February 8, 1991. A renewed Franchise Agreement is dated April 30,1997, and effective on the expiration of the original agreement on February 8, 1998. There is no dispute that the original Franchise Agreement was duly entered into by PPR and was effective at the time when McKenna became a party to the Shareholder Agreement. McKenna’s right to purchase the shares under the arbitration award is retroactive to the time of the transfer to Sosso and Croushore in 1995. At that time, too, the original Franchise Agreement was in effect. When PREA exercised its right of first refusal in September, 1998, the renewed Franchise Agreement was in effect. The district court did not specify which agreement governed PREA’s exercise of its right of first refusal. The agreements are identical, however, in their provisions respecting PREA’s right of first refusal, and in most other respects.
McKenna argues that the provision of the Pre-Incorporation Agreement subjecting share transfers to “any then effective franchise agreement” is an agreement to be bound by a future agreement that is unenforceable under In re Vylene Enterprises, 90 F.3d 1472, 1476 (9th Cir.1996). Vylene considered an agreement between a franchisee and a franchisor to enter into an unspecified future franchise agreement, and held that such an agreement to agree is too indefinite to enforce. See id. Vyl-ene did not hold that a shareholder in a franchisee cannot agree to be bound by future agreements duly entered into between the franchisee and franchisor, as when a principal authorizes an agent to enter into future agreements on his behalf.
McKenna also suggests that Sosso and Croushore could not vote the shares that were the subject of the arbitration dispute to renew the Franchise Agreement in April 1997. McKenna cites no authority that prohibits record owners from voting stock that is subject to an unresolved dispute. Moreover, the facts are unclear and disputed regarding whether McKenna consented or objected to the renewal of the Franchise Agreement. Under these circumstances, we cannot say that the district court abused its discretion when it concluded that the original Franchise Agreement was in fact “extended and renewed on April 30, 1997,” and that McKenna was bound by both the original and the renewed agreements.
4
The Franchise Agreement provides that “the right of Franchisee and Equity Holders to Transfer any equity interest in Franchisee ... shall be subject to Franchisor’s right of first refusal with respect thereto if such Transfer ... is in excess of 25%” of the Franchisee’s equity. The Franchisor must exercise this right within ten days of receiving notice “setting forth ... all of the terms and conditions of any bona fide offer relating to a proposed Transfer” of shares, and “all available information concerning the proposed transferee.”
On September 1, 1999, McKenna’s attorney sent a letter to Sosso’s and Croushore’s attorney calculating the net payment price for the shares under the *877arbitration award, and stating that McKenna “hereby agrees to tender the appropriate amount upon closing....” PPR’s September 4, 1998, letter to PREA, along with the arbitration award that was attached, set forth the terms and conditions on which McKenna had offered on September 1 to purchase the shares. PPR’s letter identifies McKenna as the proposed transferee, and describes her relationship to the company. In a facsimile dated September 14, 1998, ten days after notice of the terms of McKenna’s offer, PREA informed the interested parties that it intended to exercise its right of first refusal to purchase the shares on the same terms available to McKenna.
It does not appear that PREA previously waived its first refusal rights respecting the proposed transfer of shares to McKen-na when it did not exercise them in relation to the September 1995 share purchase agreement between McKenna and the En-gelbergs, or the March 1998 preliminary arbitration award. In 1995, PREA received notice of and consented to a transfer of shares to Sosso and Croushore, not to McKenna. The March 1998 award specified that McKenna was the proposed transferee, but did not state any terms on which she offered to purchase the shares. Neither of these communications appear to have constituted the requisite notice to PREA setting forth the terms of a bona fide offer relating to a transfer of shares to McKenna.
The record supports the conclusion that PREA exercised its right of first refusal within ten days of receiving “written notice setting forth all of the terms and conditions of a bona fide offer relating to a proposed transfer” of nearly 40% of the equity in PPR and its related companies to McKenna.
5
McKenna argues that PREA’s sole remedy for an attempt to transfer shares in breach of the Franchise Agreements would be termination of the franchise. We disagree. Paragraph 10.02 of the Franchise Agreement reads:
Any purported Transfer of ... an equity interest in Franchisee not in accordance with this Agreement shall be null and void and shall constitute a material breach of this Agreement, for which Franchisor may terminate this Agreement upon notice without opportunity to cure....
The paragraph’s plain language is permissive, not obligatory.
6
McKenna claims that PREA is collaterally estopped by its participation in the Pennsylvania proceedings from asserting its right of first refusal in these proceedings. California requires that a party asserting collateral estoppel establish five elements:
First, the issue sought to be precluded from relitigation must be identical to that decided in a former proceeding. Second, this issue must have been actually litigated in the former proceeding. Third, it must have been necessarily decided in the former proceeding. Fourth, the decision in the former proceeding must be final and on the merits. Finally, the party against whom preclusion is sought must be the same as, or in privity with, the party to the former proceeding.
Lucido v. Superior Court, 51 Cal.3d 335, 272 Cal.Rptr. 767, 795 P.2d 1223, 1225 (1990). First and second, the issue actually litigated and decided in the arbitration was McKenna’s right against Sosso and Croushore under the Shareholder Agreement, not PREA’s rights against McKenna as a prospective transferee under the Franchise Agreement. Third, even if the arbitrators had purported to decide PREA’s rights under the Franchise Agreement, that decision would not necessarily have decided who, among the parties to the arbitration, had a superior right to purchase the shares. Fourth, the order *878confirming the award is presently on appeal, and is thus not final. See People v. Sims, 32 Cal.3d 468, 186 Cal.Rptr. 77, 651 P.2d 321, 332 (1982) (judgment is final for purposes of collateral estoppel only when free from direct attack). Fifth, and finally, McKenna concedes that PREA was not a party to the arbitration, though she argues that the franchise relationship between PREA and PPR establishes privity. That argument, however, is unpersuasive.
Privity is an ill-defined concept that the California Supreme Court candidly acknowledges is “essentially a shorthand statement that collateral estoppel is to be applied in a given case” where a “sufficiently close” relationship exists between the losing party in the prior case and the party to be estopped. Id. at 486, 651 P.2d 321 (quotations omitted). At a minimum, however, privity requires an identity of interest in and control over the prior action such that the nonparty should reasonably expect to be bound. See Courtney v. Waring, 191 Cal.App.3d 1434, 237 Cal.Rptr. 233, 240 (1987); Lynch v. Glass, 44 Cal.App.3d 943, 119 Cal.Rptr. 139, 142-43 (1975) (identity of interest and appearance as a witness for losing party in prior litigation insufficient to establish privity when control was lacking). There is no evidence that PREA had an identical interest to, nor exercised any degree of control over, any party participating in the Pennsylvania proceedings.
No case directly addresses whether the franchise relationship by itself is sufficiently close generally to bind a franchisor to the results of litigation to which its franchisee is a party. In another context, California has held that the partnership relationship is insufficiently close to establish privity such that a judgment against one partner for a private tort committed in the course of partnership business will bind other partners in a subsequent proceeding. See Dillard v. McKnight, 34 Cal.2d 209, 209 P.2d 387, 391 (1949); see also Lynch, 119 Cal.Rptr. at 142 (citing Dillard). A fortiori, we believe the California courts would hold that a judgment against a franchisee arising out of a dispute among its shareholders does not bind the franchisor merely by virtue of the less intimate franchise relationship.
In reviewing the grant of the preliminary injunction, we conclude that McKen-na is unlikely to succeed in establishing that PREA is collaterally estopped from asserting its rights to purchase the shares in this suit by virtue of its limited participation in the Pennsylvania proceedings.
B
The district court found that a transfer of the stock to McKenna would allow her to “materially influence the business decisions of PPR,” and concluded that the breach of the Franchise Agreements, possible harm to PPR’s business, and the impairment of PREA’s rights to obtain an interest in PPR would threaten harm that “may not be fully remedied by money damages alone.”
If McKenna were to obtain a substantial minority stake in PPR, many business decisions would require her consent. It is not unreasonable to fear that dissension harmful to PPR’s business might result. Further, if the stock is transferred to McKenna, the transaction might be difficult to undo should PREA ultimately prevail in this litigation. The district court did not abuse its discretion in finding that PREA was threatened with irreparable harm that was sufficient to warrant an injunction, when viewed in light of PREA’s likely success on the merits.
V
McKenna contends that the Anti-Injunction Act, 28 U.S.C. § 2283, prohibits the district court from enjoining transfer of the stock that she was awarded in the Pennsylvania arbitration. The Anti-Injunction Act bars federal courts from enjoining ongoing state court proceedings except in specific and narrow circumstances. See Empire Blue Cross and *879Blue Shield v. Janet Greeson’s a Place for Us, Inc., 985 F.2d 459, 461 (9th Cir.1993). “The prohibition ... ‘cannot be evaded by addressing the order to the parties or prohibiting utilization of the results of a completed state proceeding.’ ” Los Angeles Mem’l Coliseum Com’n v. City of Oakland, 717 F.2d 470, 473 (9th Cir.1983) (quoting Atlantic Coast Line R.R. v. Brotherhood of Locomotive Eng’rs, 398 U.S. 281, 287, 90 S.Ct. 1739, 26 L.Ed.2d 234 (1970)). “[W]hether an injunction may issue under the act is a question of law reviewed de novo.” Blalock Eddy Ranch v. MCI Telecomm. Corp., 982 F.2d 371, 375 (9th Cir.1992).
A
An arbitration is a “state proceeding” for purposes of the Act if it has been ordered or its award enforced by a state court in judicial (as opposed to merely ministerial) proceedings. See Empire Blue Cross, 985 F.2d at 461-62. Conversely, “where an arbitration proceeding is private and voluntary, and the state courts have not become involved, and may never become involved, in the proceeding, the Anti-Injunction Act does not apply.” Six Clinics Holding Corp., II v. Cafcomp Sys., Inc., 119 F.3d 393, 398-99 (6th Cir. 1997) (distinguishing Empire Blue Cross).
Here, proceedings to enforce the final arbitration award are contested and ongoing before the Pennsylvania state court, and have been since McKenna brought suit to enforce the original award in March 1998. Furthermore, the arbitration that produced the final award was ordered by the Pennsylvania state court in the course of that suit. The Pennsylvania arbitration has clearly become a “state proceeding” for purposes of the Anti-Injunction Act.
B
Nevertheless, the Anti-Injunction Act does not bar one who is not a party to state proceedings, nor in privity with a party, from seeking a federal injunction against enforcement of the resulting judgment. See Imperial County, Cal. v. Munoz, 449 U.S. 54, 59-60, 101 S.Ct. 289, 66 L.Ed.2d 258 (1980). “Privity,” for purposes of the so-called “strangers to the state court proceeding” exception to the Anti-Injunction Act, has the same meaning as for purposes of collateral estoppel: one who is not bound directly by virtue of a sufficiently close relationship with a party to state proceedings is not bound indirectly by the Anti-Injunction Act. See Munoz v. Imperial County, 667 F.2d 811, 814, 814-16 (9th Cir.1982). As discussed previously, PREA is not in privity with any party to the Pennsylvania proceedings, and is not bound by the result. Under the “strangers” exception, neither is it bound under the Anti-Injunction Act.
McKenna argues that the Supreme Court implicitly abolished the judicially-created “strangers” exception in Chick Kam Choo v. Exxon Corp., 486 U.S. 140, 146, 108 S.Ct. 1684, 100 L.Ed.2d 127 (1988), in which Justice O’Connor wrote: “[A]n injunction staying state proceedings is proper only if it falls within one of the statutory exceptions” provided by the Act. McKenna also notes the reluctance of the First Circuit to invoke the “strangers” exception where it was technically applicable, “as it has been utilized so seldom by the Supreme Court that its continued vitality has even been questioned.” Casa Marie, Inc. v. Superior Court of Puerto Rico, 988 F.2d 252, 266 (1st Cir.1993) (citing Imperial County, 449 U.S. at 60-61, 101 S.Ct. 289 (Powell, J., concurring) (“I record my willingness to reconsider [the ‘strangers’ exception], It has rarely been cited and ... creates an exception ... that I think is contrary to the policy of th[e] Act.”))
The “strangers” exception was not at issue, however, in Chick Kam Choo. Nor was it controlling in Casa Marie, which was ultimately decided on Younger abstention grounds. See id. at 266-70. Notwithstanding the First Circuit’s remarks in Casa Marie, and contrary to McKenna’s *880assertions, the “strangers” exception has been regularly applied since Chick Kam Choo. See, e.g., Gottfried v. Medical Planning Servs., Inc., 142 F.3d 326, 329 (6th Cir.), cert. denied, 525 U.S. 1041, 119 S.Ct. 592, 142 L.Ed.2d 534 (1998);. Chezem v. Beverly Enters.-Texas, Inc., 66 F.3d 741, 742-43 (5th Cir.1995); Pelfresne v. Village of Williams Bay, 917 F.2d 1017, 1020 (7th Cir.1990).
Binding Supreme Court and Ninth Circuit decisions, as well as the weight of recent authority from other circuits, support the continued vitality of the “strangers” exception to the Anti-Injunction Act. One who is not a party to state proceedings, nor in privity with a party, may seek a federal injunction against enforcement of a judgement obtained in those proceedings.
VI
McKenna has appealed the district court’s decision that it lacked jurisdiction to consider her motion to vacate the preliminary injunction. This court reviews de novo a district court’s decision regarding its jurisdiction to vacate its own order during the pendency of an appeal. See Carriger v. Lewis, 971 F.2d 329, 332 (9th Cir.1992) (en banc). A district court lacks jurisdiction to modify an injunction once it has been appealed except to maintain the status quo among the parties. See McClatchy Newspapers v. Central Valley Typographical Union No. 16, 686 F.2d 731, 734-35 (9th Cir.1982); see also Flynt Distrib. Co. v. Harvey, 734 F.2d 1389, 1392 n. 1 (9th Cir.1984); Coastal Corp. v. Texas Eastern Corp., 869 F.2d 817, 819-20 (5th Cir.1989).
It is irrelevant that McKenna characterized her motion as one for relief from a judgment or order on grounds of fraud under Federal Rule of Civil Procedure 60(b). “[T]he label attached to a motion does not control its substance.” United States v. State of Oregon, 769 F.2d 1410, 1414 n. 4 (9th Cir.1985). Moreover, a preliminary injunction is not a “final judgment, order, or proceeding” that may be addressed by a motion under Rule 60(b). Fed.R.CivJP. 60(b); see 28 U.S.C. § 1292(a)(1) (orders granting preliminary injunctions are “interlocutory orders”); see also Adams v. City of Chicago, 135 F.3d 1150, 1153 (7th Cir.1998); Caravantes v. INS, 967 F.Supp. 1179, 1182 (D.Ariz.1997).
VII
The orders of the district court enjoining transfer of the disputed stock, and refusing to consider McKenna’s motion to dissolve the preliminary injunction while that injunction is on appeal are AFFIRMED. McKenna has requested sanctions against PREA for necessitating these appeals. That request is DENIED.