This matter arises out of a substantial release of diesel fuel from a freight locomotive, known as MEC 506, in the Ayer railyard on August 8 and August 9, 2006. A Superior Court jury convicted the codefendants, Pan Am Railways, Inc., Springfield Terminal Railway Company (Springfield), Boston & Maine Corporation (B&M), and Maine Central Railroad Company (Maine Central) of failing to notify the Department of Environmental Protection (DEP) immediately of the release as required by G. L. c. 2IE, §§ 7, 11. The defendants appeal. We affirm.
1. Background. We recite the evidence as it developed at trial.
a. The corporate defendants. The four corporate defendants compose an integrated freight rail transportation operation. Pan Am Railways, Inc., formerly known as Guilford Transportation, *24Inc., is the parent company of B&M, Springfield, and Maine Central.2 *B&M owns the Ayer railyard, and Springfield operates it. Maine Central owns the locomotive, MEC 506, from which the release occurred. The four corporations share all but one of the same officers and directors. The four corporations coordinate their operations; train cars bearing the railroads’ insignias are frequently mixed, and employees of all four corporations do not ' meaningfully distinguish between them. Many official corporate documents and employee business cards bear the names and insignias of two or more of these entities. Accordingly, we will refer to them collectively as Pan Am hereafter.
b. The release. On August 8, 2006, MEC 506, a diesel-powered freight locomotive with a fuel capacity of 3,750 gallons, was stationary in the Ayer railyard. Between 5:00 p.m. and 7:00 p.m., MEC 506 began leaking diesel fuel onto the ground. Two Pan Am employees noticed the odor of diesel fuel at around 7:00 p.m. and reported the odor to their superiors between 8:30 p.m. and 9:00 p.m. About one hour later, after finishing an unrelated task, the two employees observed MEC 506 spilling fuel “like ... [a] waterfall.” They shut down the engine and largely stopped the leak. One of the employees then reported the release to train dispatcher Gary Munsey and to Pan Am’s power control.3 In these reports, the employee estimated that hundreds of gallons of fuel had spilled into the yard.4
Pan Am employees worked throughout the night attempting to collect the spilled fuel with absorbent pads. MEC 506 appears to have continued leaking intermittently throughout the night, and at least one witness, a train engineer, observed leaking between 6:00 a.m. and 7:00 a.m. on August 9. The engineer *25visually estimated that the spill affected a ground surface area of thirty feet by sixty feet. At 6:30 a.m., a Pan Am corporate vice-president called a train master and asked about the spill. The train master, based on his observations of the railyard from approximately three hours earlier, told the vice-president that an estimated 100 gallons of fuel had spilled.
Clean-up operations continued throughout the morning of August 9. Fuel from MEC 506 had saturated the ballast — crushed rock used to support railroad track — and underlying soil around the locomotive. Pan Am employees excavated this ballast and soil and removed it from the site in several fifty-five-gallon drums. These employees replaced the excavated material with new ballast. Heavy machinery facilitated these operations, which continued throughout August 9.
At 2:45 p.m., on August 9, an anonymous informant alerted DEP to the spill by telephone. None of the four corporate defendants had made a previous report of the release to DEP. About seventeen hours had passed since Pan Am employees had first reported the spill to their superiors. Following the anonymous telephone call alerting DEP to the spill, DEP personnel contacted Pan Am management. Several corporate representatives were later present at the scene of the release, including Pan Am’s environmental compliance officer, John Collins.
Personnel from DEP, as well as from the Ayer fire department and the Federal Railroad Administration (FRA), responded to the scene. Throughout the remainder of the day on August 9 and into August 10, these personnel supervised the excavation and disposal of soil contaminated by the spill.
At the same time, FRA inspectors began investigating MEC 506’s fueling and travel history. Based on information received from Pan Am and a series of simple mathematical calculations, an FRA inspector concluded that 947 gallons of fuel were unaccounted for following the spill.5
*26In the aftermath of the spill, Pan Am engaged Environmental Resource Management (ERM), an environmental consultancy, to assist in remedying the spill’s effects. ERM oversaw the excavation of a pit, approximately sixty feet by twenty-five feet, of potentially contaminated soil and the subsequent disposal of the soil. ERM oversaw the installation of groundwater monitoring wells on and around the railyard and analyzed soil samples from the site. Ultimately, DEP concluded that no contamination of groundwater or other harm to the local environment occurred as a result of the release.
c. Pretrial proceedings. The parties made several pretrial motions, including discovery motions by Pan Am and several motions in limine. The judge denied Pan Am’s motion to exclude certain background testimony by a DEP employee about G. L. c. 21E, its implementing regulations, DEP’s interpretation of its mandates, and DEP reporting procedures. The judge also denied both Pan Am’s motion to prevent an ERM witness from testifying about Pan Am’s prior releases and engagement of ERM to assist in remedying those releases and its motion to exclude testimony about Pan Am’s delinquency in paying for services rendered by ERM.
The Commonwealth moved to exclude any statements by John Collins, Pan Am’s environmental compliance officer, and to exclude evidence that he had invoked his rights against self-incrimination under the Fifth Amendment to the United States Constitution and art. 12 of the Massachusetts Declaration of Rights. Collins had previously announced, through counsel, his intent to invoke these rights if called to testify. The Commonwealth refused to grant him immunity. After hearing from Collins in camera, the judge concluded that Collins had a good faith basis for asserting his privilege.
After hearing additional argument from the parties, the judge allowed the Commonwealth’s motion to exclude Collins’s statements and any reference to his invocation of his rights against *27self-incrimination. Subsequently, Pan Am’s motion requesting that the judge grant judicial immunity or order the Commonwealth to apply for statutory immunity for Collins was denied. Collins did not testify at the trial, and neither side was permitted to elicit any statements he had made to other trial witnesses.
d. The trial. The Commonwealth presented several witnesses employed by Pan Am, DEP, the FRA, and ERM to testify to the above facts. In addition, a DEP witness testified, over Pan Am’s objection, about DEP’s responsibilities with respect to c. 21E and other environmental laws. He also testified about the Ayer railyard’s proximity to “sensitive receptors.” When asked to define a “sensitive receptor,” the witness gave the example of a school because releases of hazardous material could affect schoolchildren. He also discussed a “priority resource map” prepared by DEP to identify “sensitive receptors” near the Ayer railyard. This map was admitted as a trial exhibit.
A former ERM project manager who led the response to this release also testified over objection that Pan Am had engaged ERM to assist with other releases. The witness also testified, again over objection, that ERM had difficulty in collecting payment from Pan Am for ERM’s services related to these remedial efforts.
After the Commonwealth rested, Pan Am’s motion for required findings of not guilty was denied. Pan Am then rested without presenting evidence. Following lengthy instructions, the jury convicted on all counts. The jury specified, using special verdict slips, that they based their verdict on each count on a finding of “corporate responsibility for collective knowledge of employee(s)/agent(s). ”6
e. Sentence. The judge sentenced each defendant on its first count to pay a fine of $100,000, plus a $25,000 surfine, within thirty days. On its second count each defendant was placed on probation for three years with several special conditions, includ*28ing restrictions on disposition of assets and a bar on compensation for any personnel exceeding $100,000 in a twelve-month period until payment of the imposed fines. Pan Am paid the fines into an interest-bearing account held jointly with the Attorney General pending the outcome of its appeals. The judge required the defendants’ corporate officers to sign the conditions of probation in their official capacities.
f. Posttrial proceedings. After filing its notice of appeal, Pan Am moved to stay execution of the sentences. The judge denied the motion and ordered payment. Pan Am sought single justice relief from this court and the Supreme Judicial Court. See Mass. R.Crim.P. 31(a), as appearing in 378 Mass. 902 (1979); Mass. R.A.P. 6, as amended, 378 Mass. 930 (1979).7 Single justices of both courts denied relief, and Pan Am appealed. A panel of this court affirmed the single justice of this court, Commonwealth v. Springfield Terminal Ry. Co., 77 Mass. App. Ct. 225 (2010), and the Supreme Judicial Court denied further appellate review, 458 Mass. 1104 (2010).
g. Appeal. Pan Am appeals from the judgments, arguing these points: (1) the judge erroneously failed to instruct the jury that conviction under G. L. c. 21E, § 11, requires a wilful violation, (2) the judge erroneously instructed that G. L. c. 21E, § 11, permits conviction of a corporation based on collective corporate knowledge, (3) Massachusetts law does not permit a judge to order probation for a corporation, (4) the judge gave erroneous instructions on piercing the corporate veil, (5) the judge gave erroneous instructions on the statutory definition of “day” in G. L. c. 21E, § 11, and (6) the judge erred in various evidentiary rulings.
2. The statutory scheme. General Laws c. 21E, the Massachusetts Oil and Hazardous Material Release Prevention Act, was enacted in 1983. See St. 1983, c. 7, § 5. Among other things, it requires that responsible persons, identified by G. L. c. 21E, § 5, notify DEP immediately as soon as the responsible *29person acquires knowledge of a release of oil or hazardous material. G. L. c. 21E, § 7.8 Failure to notify is criminally punishable under G. L. c. 21E, § 11.9
The Legislature instructed DEP to promulgate “regulations establishing thresholds below which notification shall not be required by [§ 7], and procedures for giving notification required pursuant to [§ 7].” G. L. c. 21E, § 7, as amended by St. 1992, c. 133, § 303. It is uncontested that, pursuant to regulation, the relevant amount threshold for a spill of diesel fuel was ten gallons, with a requirement of notification to DEP as soon as possible, but not more than two hours, after obtaining the required knowledge of the spill. See 310 Code Mass. Regs. § 40.0311 (1999); 310 Code Mass. Regs. § 40.1600 (2006).10
3. Mens rea. Pan Am argues that the judge improperly instructed that the Commonwealth could meet its burden by proving that Pan Am had the required knowledge of the spill and simply failed to notify DEP within two hours of acquiring this knowledge. Pan Am claims that the judge should have read a requirement of a wilful failure to notify into § 11 and instructed accordingly. The judge declined to give such an instruction as Pan Am requested, and Pan Am objected. As a result, we review *30to determine whether the failure to provide the requested instruction was prejudicial error. See Commonwealth v. Zimmerman, 441 Mass. 146, 150 (2004).
The statute criminalizing failure to report a qualifying release to DEP plainly requires knowledge of such a release and the absence of notification to DEP in order to establish criminal liability. Because § 11 incorporates § 7 by reference, the knowledge element of the notification duty under § 7 is a material element of § 11 criminal liability. See G. L. c. 21E, § 11 (“[A] person violating any provision of [G. L. c. 21E, § 7,] shall be punished”); G. L. c. 21E, § 7 (“[A]s soon as [a site owner or operator] has knowledge of a release or threat of release of oil or hazardous material, [he] shall immediately notify [DEP] thereof” [emphasis added]).11
Accordingly, the Commonwealth, in order to establish the § 11 criminal liability at issue here, was required to prove only that a defendant had the required knowledge of the release and failed to notify DEP within the prescribed time limit.12 To the extent that Pan Am argues that this court should supplement the legislatively enacted text of § 11 with the word “wilfully,” a word that appears nowhere in § 7 or § 11, the argument is better addressed to the Legislature, and we decline to do so. There was no error in the judge’s instructions.
4. Collective corporate knowledge. Pan Am argues that the judge improperly instructed that the Commonwealth could establish Pan Am’s knowledge of the release through collective corporate knowledge — as the judge put it, “the totality of what all of [a corporation’s] employees and agents [knew] within *31the scope of their employment.”13 Pan Am argues that corporate criminal liability under § 11 arises only when there is criminal liability by an agent or employee imputed to the corporation by the doctrine of respondeat superior.14 We review the instruction and the verdict slips for prejudicial error. See Zimmerman, 441 Mass. at 150.
Where a mens rea requirement of mere knowledge attaches to a material element of a statutorily-created crime unknown at common law, “[a] collective knowledge instruction is entirely appropriate in the context of corporate criminal liability.” United States v. Bank of New England, N.A., 821 F.2d 844, 856 (1st Cir.), cert. denied, 484 U.S. 943 (1987) (Bank of New England). In Commonwealth v. Life Care Centers of America, Inc., 456 Mass. 826 (2010) (Life Care), the court acknowledged this principle. Id. at 836, citing Bank of New England, supra.15 Because the offense in Bank of New England was a statutorily-created crime, and because “the mens rea at issue in [Bank of New England) was essentially only the requirement of knowledge,” the collective knowledge instruction given there was appropriate as a matter of Massachusetts law.16 Life Care, supra.
*32We interpret Life Care and Bank of New England, taken together, to mean that the Commonwealth may establish a corporation’s knowledge, for purposes of imposing criminal liability, through collective knowledge of the corporate defendant’s agents or employees when (1) the charge is a statutorily created crime unknown to the common law, and (2) the mens rea required as a material element of the crime is mere knowledge.17 So interpreted, the cases do not limit liability to instances of respondeat superior.
Therefore, Life Care and Bank of New England permit the Commonwealth to meet its burden with respect to a corporate defendant charged with a statutorily-created crime having a mens rea of knowledge by showing either (1) collective corporate knowledge or (2) respondeat superior. This interpretation does not run afoul of the requirement of Life Care that the Commonwealth prove that an agent or employee had the requisite mens rea in order to convict a corporate defendant of a crime requiring proof of wanton or reckless conduct or of intentional or wilful conduct. See note 16, supra.
*33The availability of collective knowledge to establish corporate criminal liability stands in accord with existing Massachusetts law regarding the use of collective knowledge to establish civil liability.18 See Life Care, 456 Mass. at 834 (“[I]n developing doctrine of corporate criminal liability, we have relied at times on agency concepts drawn from civil law”), citing Commonwealth v. Beneficial Fin. Co., 360 Mass. 188, 290-294 (1971), cert. denied, 407 U.S. 914 (1972). It is well established that, for purposes of civil liability that requires a plaintiff to show a corporation’s mere knowledge, a plaintiff can make such a showing based on the collective knowledge of the corporation’s agents or employees. See Sarna v. American Bosch Magneto Corp., 290 Mass. 340, 343 (1935), and cases cited; Paloeian v. Day, 299 Mass. 586, 591 (1938), and cases cited; Birbiglia v. Saint Vincent Hosp., Inc., 427 Mass. 80, 87 (1998). See also Sunrise Properties, Inc. v. Bacon, Wilson, Ratner, Cohen, Salvage, Fialky & Fitzgerald, P.C., 425 Mass. 63, 66-68 (1997) (corporation had knowledge of a fact, as matter of law, when agent had knowledge of same fact in course and scope of agency). But where civil liability requires a showing of specific intent or another mens rea other than mere knowledge, the plaintiff cannot meet its burden by aggregating the intent of the corporate defendant’s agents or employees. See Birbiglia, 427 Mass. at 87 n.5. See also Life Care, 456 Mass. at 833-836.
Here, §§ 7 and 11 create a crime unknown at common law and specify mere knowledge as the operative mens rea. The judge therefore properly instructed that the collective knowledge of Pan Am’s agents or employees could establish Pan Am’s *34knowledge of the release for purposes of § 11 criminal liability.19
In addition, contrary to Pan Am’s contention, the judge’s instructions did not mislead the jury by implying that collective corporate knowledge by itself constituted a basis for corporate criminal liability. The instructions appropriately recited the material elements of § 11 criminal liability for an unreported release of diesel fuel, including both the required knowledge of the release and a failure to report it to DEP within two hours in circumstances where the volume of the release was ten or more gallons. The instructions further distinguished, appropriately and clearly, between corporate liability based on Pan Am’s agents or employees violating § 11 (i.e., respondeat superior liability, see notes 6 & 14, supra) and corporate liability based on the corporation itself violating § 11 because, through its agents and employees, it had the necessary knowledge of the release and failed to notify DEP in time. There was no error in the instructions.20
5. Corporate probation. Pan Am argues that the judge had no statutory authority to place the corporate defendants on probation. Pan Am insists that the term “person,” as used in the relevant statute, G. L. c. 276, § 87,21 does not encompass corporations. We disagree.
*35The statute governing construction of the General Laws, G. L. c. 4, § 7, provides, “[i]n construing statutes the following words shall have the meanings herein given, unless a contrary intention clearly appears: . . . Twenty-third, ‘Person’ or ‘whoever’ shall include corporations, societies, associations and partnerships.” Accordingly, unless a contrary intention clearly appears in G. L. c. 276, § 87, that statute permits the probationary sentence ordered by the judge. See Commonwealth v. Angelo Todesca Corp., 446 Mass. 128, 135-136 (2006) (“[B]y including corporations within the general statutory definition of ‘person,’ the Legislature evinced a general intent to hold corporations legally accountable for their actions. Because no intention to exclude corporations from the definition of ‘persons’ or ‘whoever’ appears in G. L. c. 90, we conclude that a corporation may be criminally liable for violation of [the vehicular homicide statute,] G. L. c. 90, § 24G[b\ . . .” [footnote omitted]).
No such contrary intention appears in the probation statute. Although Pan Am points to various aspects of that statute, such as references to placing probationers “in the care of [a] probation officer,” age of the probationer, and offenders who have committed certain sex abuse crimes, see G. L. c. 276, § 87, these minor inconsistencies do not amount to sufficient contrary legislative intent. Similar references to “defendant(s),” “he,” or “she,” or other language intended to alter the meaning of the statute as applied to natural persons, appear throughout the Commonwealth’s criminal statutes. See, e.g., G. L. c. 90, § 24G(c) (referring to “right to operate” a motor vehicle of a “defendant” charged with violating G. L. c. 90, § 24G[¿>]), as amended by St. 1986, c. 620, § 16. Because it is well established that such references do not evidence legislative intent to exclude corporations from the definition of “person” as used in those criminal statutes, see, e.g., Angelo Todesca Corp., supra, it follows that similar language in G. L. c. 276, § 87, also does not evidence this intent to exclude corporations from its operation.22
Nor are we convinced otherwise by the 2003 enactment of *36G. L. c. 21L, a criminal statute known as the Environmental Endangerment Act, which includes a specific directive for sentencing judges to impose a special probation condition on corporations in certain circumstances. General Laws c. 21L, § 3(a), authorizes a special probation condition, mandatory for subsequent offenses under G. L. c. 21L, § 2(b)(2), and discretionary for first time offenses, that a defendant organization pay for an environmental audit (the recommendations of which the court is empowered to enforce). The statute deems this special condition sufficiently important that it authorizes a court to impose “a term of probation that is longer than the term otherwise permitted by law, if the court determines that the longer term is necessary to implement the environmental audit.” G. L. c. 21L, § 3(e), inserted by St. 2003, c. 26, § 123. Accordingly, we see nothing in the enactment of G. L. c. 21L, with specific authorization for corporate probation subject to a statutorily prescribed special condition in certain cases, to affect the conclusion that a judge may impose standard probation conditions on a corporation in other cases, as she may on any legal person, pursuant to G. L. c. 276, § 87.
Here, the judge’s decision to suspend part of Pan Am’s sentence and impose probation was therefore well within her statutorily authorized discretion.23 Similarly, her decision to require certain officers of Pan Am to sign the conditions of *37probation in their respective capacities as corporate officers was entirely appropriate. See Beneficial Fin. Co., 360 Mass. at 264 (a corporation “has no existence separate and distinct from those whom it has clothed with authority and commissioned to act for it whether such individuals are directors, officers, shareholders or employees”). There was no error.
6. Piercing the corporate veil. Pan Am argues that the judge erroneously instructed that “[t]he knowledge and/or criminal conduct of one corporation may be imputed to another corporation where there is confused intermingling of activity of two or more corporations engaged in a common enterprise with substantial disregard of the separate capacity in which the various corporations and their respective representatives are acting.” Pan Am argues that these instructions misstated the law of piercing the corporate veil in that the judge omitted “the necessity of finding that the corporation whose veil would be pierced exercised some form of pervasive control over the other and that there is some fraudulent or injurious consequence of the intercorporate relationship.” The judge denied Pan Am’s request to add this matter to the instructions, and Pan Am objected. As a result, we review for prejudicial error. See Zimmerman, 441 Mass. at 150.
“In the environmental context, as in other contexts, corporate veils are pierced only in ‘rare particular situations,’ and only when an ‘agency or similar relationship exists between the entities.’ ” Scott v. NG US 1, Inc., 450 Mass. 760, 767 (2008), quoting from My Bread Baking Co. v. Cumberland Farms, Inc., 353 Mass. 614, 619, 620 (1968) (My Bread). There are two separate and distinct categories of such situations: (1) pervasive control by the parent of the subsidiary coupled with fraudulent or injurious consequence of the relationship; and (2) confused intermingling of corporate activity disregarding formal corporate separation. Scott, 450 Mass. at 767, quoting from My Bread, 353 Mass. at 619. See Beneficial Fin. Co., 360 Mass. at 290-291. *38Proof of the characteristics of either of these categories permits piercing the corporate veil. See Attorney Gen. v. M.C.K., Inc., 432 Mass. 546, 557 (2000) (M.C.K.) (rejecting claim that fraud or deception was required before disregarding corporate form); Scott, 450 Mass. at 768-769 (considering separately “confused intermingling” basis for piercing veil, which does not involve a claim of “fraudulent or injurious consequence”).
In M.C.K., the court considered the twelve factors identified in Pepsi-Cola Metro. Bottling Co. v. Checkers, Inc., 754 F.2d 10, 14-16 (1st Cir. 1985), as proper guidance for a fact finder’s decision whether to disregard the corporate form.24 M.C.K., 432 Mass. at 555 n.19. Beneficial Fin. Co. articulated a different list of relevant factors.25 Beneficial Fin. Co., 360 Mass. at 291-292. Finally, M.C.K. also “recognized . . . that frustration of a statutory scheme, when coupled with pervasive control and confused intermingling of activity and assets, supported corporate veil piercing.” Scott, 450 Mass. at 769 n.16.
Pan Am makes two interrelated complaints about the judge’s instructions. First, Pan Am argues that the judge erroneously failed to instruct that piercing the corporate veil requires a showing of fraudulent purpose or fraudulent conduct in the parent’s control of the subsidiary. The Supreme Judicial Court has repeatedly stated since My Bread that two separate and distinct means of piercing the corporate veil exist and that only *39one of them requires a showing of fraud. See My Bread, 353 Mass. at 619; Beneficial Fin. Co., 360 Mass. at 290-291; M.C.K., 432 Mass. at 557; Scott, 450 Mass. at 767-768. The judge therefore properly declined to give the instmction because fraudulent purpose or conduct is not a necessary element of imposing derivative liability, whether criminal or civil, on a parent corporation.
Second, and more generally, Pan Am claims that the judge erroneously instructed the jury to consider the factors in Beneficial Fin. Co., which do not include fraudulent purpose or conduct, instead of those in M.C.K., which do include fraud. We conclude that, in light of the evidence presented, she had the discretion to instruct as she did. See Commonwealth v. Monteiro, 51 Mass. App. Ct. 552, 559 (2001) (a judge always retains discretion to “adapt a jury charge to conform appropriately to the evidence at hand”).
Many of the M.C.K. factors had no relevance to the facts presented at trial. Here there was no question of insolvency or thin capitalization, no allegation of deliberate abuse of the corporate form by a single dominant shareholder, and no allegation that Pan Am used its subsidiaries to promote or engage in fraudulent activities. Contrast note 24, supra. Accordingly, the judge could conclude, within her discretion, that instructions reciting the M.C.K. factors would confuse the jury and not help them resolve the issues presented at this trial.
In contrast, the Beneficial Fin. Co. factors more closely tracked the evidence presented in this trial. Beneficial Fin. Co. is still good law. The judge therefore had the discretion to instruct along the lines of those relevant factors. There was no error in the judge’s instructions on piercing the corporate veil.
7. Statutory definition of “day. ” Pan Am claims that the judge improperly instructed the jury that the word “day,” as used in G. L. c. 2IE, § 11, means a calendar day, not any given continuous twenty-four hour period. Consequently, Pan Am argues, only one conviction per defendant was possible, rather than two, for the relevant period from the evening of August 8 through the afternoon of August 9. We are not persuaded. We review again for prejudicial error. See Zimmerman, 441 Mass. at 150.
*40“[W]e think that the word ‘day’ means a calendar day. . . . It has generally been held that the word ‘day’ when not qualified means a calendar day.” Booker v. Chief Engr. of Fire Dept. of Woburn, 324 Mass. 264, 266 (1949), collecting cases, including The Pocket Veto Case, 279 U.S. 655, 679 (1929), and Opinion of the Justices, 291 Mass. 572, 577 (1935).26 Unless § 11 evidences clear intent to depart from this long-standing rule, we will not interpret it as doing so. See Fordyce v. Hanover, 457 Mass. 248, 258 (2010) (statutes construed in light of common-law definitions absent clear intent to deviate).
Pan Am argues that the Legislature demonstrated such intent by using the phrase “calendar days” in G. L. c. 21E, § 3A(/)(2), instead of the unadorned “day” used in § 11. Section 3A(/)(2) sets out a period of ninety “calendar days” for other potentially liable persons under c. 21E to comment on a settling party’s c. 21E settlement agreement with the Commonwealth. G. L. c. 21E, § 3A(/)(2), as amended by St. 1998, c. 206, § 19.27 We read “calendar day[]” in this provision as simply distinguishing the ninety-calendar-day comment period from a period defined by business days, as set out by other statutes limiting time periods for comment, objection, or response. Contrast, e.g., G. L. c. 7, § 55(a) (“An agency shall not make any privatization contract and no such contract shall be valid if, within thirty business days after receiving the certificate required by section fifty-four, the state auditor notifies the agency of his objection” [emphasis added]), as amended by St. 1998, c. 158, § 2; G. L. c. 119A, § 12(ifc); G. L. c. 149, § 44D(4).
We discern insufficient legislative intent to deviate from the established meaning of “day” as a calendar day when used without a modifier such as “business.” We therefore interpret *41the use of “day” in § 11 in conformity with this long-standing definition. The judge’s instruction was quite proper.
8. Evidentiary rulings. Pan Am claims as error several rulings on motions in limine. Such evidentiary rulings are committed “to the sound discretion of the trial judge, and we review only for abuse of that discretion.” Commonwealth v. Arrington, 455 Mass. 437, 441 n.6 (2009), citing Commonwealth v. Gonzalez, 443 Mass. 799, 805 (2005). We are unpersuaded that the judge abused her discretion in any of these rulings.
a. Statements of John Collins. Pan Am argues that the judge abused her discretion by not permitting Pan Am to introduce potentially exculpatory out-of-court statements made by Collins.28 We are not persuaded.
Pan Am presents this issue as a straightforward application of the well-established rule that “declarations out of court may be admissible to prove the state of mind or intent of a person when it is a material issue.” Commonwealth v. Magraw, 426 Mass. 589, 594 (1998). See Mass. G. Evid. § 803(3)(B) (2011), and cases cited. But this rule was not the only consideration. Instead, the judge confronted the more complex and sensitive question whether the Commonwealth29 or Pan Am could elicit Collins’s statements in light of his invocation of his Fifth Amendment30 privilege.
This question presented serious issues of potential prejudice to both sides. See Commonwealth v. Gagnon, 408 Mass. 185, 197-198 (1990) (evidence that a witness exercises his Fifth Amendment right “produce[s] no relevant evidence, while inviting the jury to engage in unwarranted and impermissible speculation”). Admission of any hearsay statement entitles the *42opposing party to attack the declarant’s credibility. See Commonwealth v. Mahar, 430 Mass. 643, 649 (2000); Mass. G. Evid. § 806. Any such attack on the credibility of a witness who invokes his Fifth Amendment privilege could impermissibly bring the exercise of that right to the attention of the jury, see Gagnon, supra, or otherwise “risk . . . confusing jurors by diverting their attention to wholly collateral matters involving persons not on trial.” Commonwealth v. Rosa, 422 Mass. 18, 22 (1996). See Mass. G. Evid. § 403.
The judge could therefore conclude, within her discretion, that any introduction, by either party, of Collins’s statements about his knowledge of the quantity of the release would lead to a collateral trial on the issues of Collins’s credibility and knowledge, improperly risking jury confusion. Moreover, the judge could similarly conclude that any collateral inquiry into Collins’s credibility could have placed his absence from the trial and his Fifth Amendment invocation before the jury, inviting undue speculation and potential prejudice to both sides.31 The judge properly exercised her discretion when she excluded any statement by Collins.32
b. DEP employee’s testimony. Pan Am argues that the judge abused her discretion in permitting a DEP employee to testify about G. L. c. 21E, the relevant implementing regulations, Pan Am’s legal duties, and the critical role that notification plays in the enforcement scheme. Pan Am asserts that the evidence was irrelevant, prejudicial, and presented by an unqualified witness. We disagree.
Relevant and necessary background evidence is admissible so long as its probative value outweighs its prejudicial effect. *43Commonwealth v. John, 442 Mass. 329, 337-338 (2004). In particular, where relevant, the judge has discretion to permit background testimony from a representative of a regulatory agency about how the agency interprets and carries out its mandates. Commonwealth v. Mimless, 53 Mass. App. Ct. 534, 543-544 & n.7 (2002).
We discern no abuse of the judge’s considerable discretion to permit this testimony. The record reveals that the judge, in ruling on Pan Am’s numerous objections, carefully cabined the witness’s testimony to ensure that it presented only relevant context derived from the witness’s area of expertise. There was no error. Moreover, Pan Am, on cross-examination, neutralized any potential prejudice by eliciting DEP’s conclusion that this release ultimately caused no environmental harm.
c. Prior bad acts evidence. Pan Am claims that the judge abused her discretion in permitting an ERM employee to testify about Pan Am’s delinquency in paying bills for environmental remediation services rendered by ERM for prior releases. Pan Am argues that this testimony constituted impermissible propensity evidence.33 We disagree.
Evidence of a defendant’s prior bad acts to show bad character or propensity to commit the crime charged is inadmissible. Commonwealth v. Helfant, 398 Mass. 214, 224 (1986). See Mass. G. Evid. § 404(b). But a judge has the discretion to allow prior bad acts evidence for a permissible purpose, such as to demonstrate motive, identity, knowledge, or absence of mistake or accident. Helfant, 398 Mass. at 224-225.
Here, the judge permitted the Commonwealth to elicit testimony that ERM had difficulty collecting payment for its services in remedying releases at other Pan Am facilities in order to show “knowledge and motive.” We conclude that Pan *44Am’s knowledge of the proper procedure for reporting and remedying similar releases and its potential monetary motive for not reporting the release at issue here were proper purposes for admitting this evidence. There was no error. Moreover, the judge cured any potential prejudice when she carefully instructed, both during the testimony and in her ultimate instructions, that the jury could not consider this evidence for propensity purposes.
9. Conclusion. We have no occasion to disturb the judgments.
Judgments affirmed.
Pan Am Railways, Inc., has other corporate subsidiaries that are not parties to these cases.
“Power control” is an operational unit of a railroad responsible for dispatching and tracking locomotives.
At trial, the train dispatcher, Munsey, denied receiving this report. Munsey also identified several corporate contingency plans effective as of August, 2006, which prescribed procedures for remedying a fuel spill and reporting it to the appropriate corporate and government officers. It does not appear that he, or any other Pan Am employee, activated these procedures on August 8 or August 9.
The FRA inspector explained his calculation in detail, using a series of conservative assumptions. Pursuant to Pan Am’s instructions for fueling locomotives, MEC 506 had been fueled with approximately 3,350 gallons of fuel, approximately 400 gallons less than its capacity, on August 5, 2006. Between August 5 and August 8, MEC 506 traveled 284 miles, expending 852 gallons of fuel. The FRA inspector further assumed that MEC 506 idled during all nontraveling hours during this period, a total of ninety hours, and *26thereby expended 451 gallons of fuel. Pan Am records showed that MEC 506 had 1,000 gallons of fuel remaining on August 9 in its main fuel tank and another 100 gallons of fuel in an “ecology tank.” Accordingly, Pan Am’s records can properly account for 2,403 gallons of fuel, leaving 947 gallons of fuel unaccounted for. A Pan Am employee testified that this method would yield an effective estimate of how much fuel had spilled.
Each special verdict slip listed, as another possible basis for guilt, “corporate responsibility for crime(s) of employee(s)/agent(s)’’ — i.e., liability under a theory of respondeat superior. See note 14, infra. The jury were instructed that they must consider each of the two theories, and that they could convict under either or both. The jury did not find guilt on any count under the respondeat superior theory.
Effective October 1, 2009, amendments to the above rules changed the procedure available to parties after a trial judge acts on a motion for a stay. See Mass.R.Crim.P. 31, as appearing in 454 Mass. 1501 (2009); Mass.R.A.R 6, as appearing in 454 Mass. 1601 (2009). We apply the earlier versions of the rules, as they were in effect when the relevant events occurred. Commonwealth v. Cohen (No. 2), 456 Mass. 128, 129 n.3 (2010).
In relevant part, G. L. c. 21E, § 7, as amended through St. 1998, c. 206, § 27, reads:
“Any owner or operator of a site or vessel, and any person otherwise described in [§ 5(a)], ... as soon as he has knowledge of a release or threat of release of oil or hazardous material, shall immediately notify [DEP] thereof.”
In relevant part, G. L. c. 21E, § 11, as amended through St. 2004, c. 251, § 8, reads:
“In addition to liability for [certain] costs incurred by the Commonwealth [related to the release] . . . (c) a person violating any provision of [§ 7] shall be punished by a fine of not more than one hundred thousand dollars, or by imprisonment in the state prison for not more than twenty years or in a jail or house of correction for not more than two and one-half years, or both, for each such violation. Each day such violation occurs or continues shall be considered a separate violation.”
The judge instructed that the knowledge required for conviction includes both knowledge that the release occurred and knowledge that it was ten or more gallons. Whether the latter element of knowledge is in fact demanded by the statute or regulations has not been made an issue before us, and our decision does not depend on its resolution.
“[K]nowledge by the accused of the facts giving rise to criminality” is a “blameworthy condition of the mind.” Commonwealth v. Buckley, 354 Mass. 508, 510, 511 (1968), quoting from Commonwealth v. Ober, 286 Mass. 25, 30 (1934). Therefore, contrary to Pan Am’s claims on appeal, § 11 does not impose strict criminal liability, and Pan Am’s arguments about the seriousness of the penalties § 11 imposes and its status as a “public welfare offense” or an “infamous crime” are therefore irrelevant. Contrast, e.g., Commonwealth v. Tart, 408 Mass. 249, 264-265 (1990); Morissette v. United States, 342 U.S. 246, 255-257 (1952).
A similar Federal statute governing releases into waters under Federal jurisdiction, the Water Pollution Control Act, has been interpreted the same way. Apex Oil Co. v. United States, 530 F.2d 1291, 1295 (8th Cir.), cert. denied, 429 U.S. 827 (1976).
Pan Am also complains of the special verdict slips that invited the jury to find Pan Am guilty based on “corporate responsibility for collective knowledge of employee(s)/agent(s).”
Under this doctrine, the Commonwealth establishes a corporation’s criminal liability by proving that “(1) an individual committed a criminal offense; (2) at the time of the offense that individual was involved in a corporate project; and (3) that individual had been vested with authority to act for the corporation with respect to that project.” Commonwealth v. Life Care Centers of America, Inc., 456 Mass. 826, 833 (2010). The jury in this case were instructed on this theory but declined to find guilt based on it. See note 6, supra.
The Supreme Judicial Court had previously in a civil case acknowledged Bank of New England as stating the rule for imputation of knowledge of employees to a corporation in the criminal context. See Sunrise Properties, Inc. v. Bacon, Wilson, Ratner, Cohen, Salvage, Fialky & Fitzgerald, P.C., 425 Mass. 63, 68 (1997).
In contrast, the intent necessary for wilfulness and the disregard necessary for negligence or recklessness cannot be aggregated for purposes of corporate criminal liability. See Commonwealth v. Beneficial Fin. Co., 360 Mass. 188, 260-271 (1971), cert. denied, 407 U.S. 914 (1972), and cases cited (specific intent); Commonwealth v. Angelo Todesca Corp., 446 Mass. 128, 137 (2006) (vehicular homicide); Life Care, 456 Mass. at 832 (wanton or reckless conduct). In Life Care, the court held that the Commonwealth could not prove wanton or reckless conduct of a corporation charged with involuntary manslaughter *32by aggregating the merely negligent acts and omissions of its agents and employees. Id. at 833-834. The court concluded that corporate criminal liability for crimes requiring a mens rea of recklessness or intent could only rest on a theory of respondeat superior. Ibid.
This interpretation also accords with the weight of Federal authority. Where criminal liability requires a showing of knowledge only, collective knowledge is an appropriate vehicle of proof. See, e.g., Riss & Co. v. United States, 262 F.2d 245, 250 (8th Cir. 1958); United States v. Ladish Malting Co., 135 F.3d 484, 492-493 (7th Cir. 1998); United States v. Sawyer Transport, Inc., 337 F. Supp. 29, 30-31 (D. Minn. 1971), aff’d, 463 F.2d 175 (8th Cir. 1972); United States v. T.I.M.E.-D.C, Inc., 381 F. Supp. 730, 738-739 (W.D. Va. 1974). See also United States v. Philip Morris USA, Inc., 566 F.3d 1095, 1122 (D.C. Cir. 2009) (acknowledging collective knowledge as appropriate vehicle for proof of mere knowledge), cert. denied, 130 S. Ct. 3501 (2010); United States v. LBS Bank-N.Y., Inc., 757 F. Supp. 496, 501 n.7 (E.D. Pa. 1990) (same). But where criminal liability requires a showing of intent or recklessness, collective intent or knowledge is not an appropriate vehicle of proof. See, e.g., Bank of New England, 821 F.2d at 855-856 (for subset of material elements requiring wilfulness mens rea instead of mere knowledge, only respondeat superior is appropriate vehicle for proof of corporate mens rea); Philip Morris USA, Inc., 566 F.3d at 1122 (collective intent inappropriate to show specific intent); United States v. Science Applications Intl. Corp., 626 F.3d 1257, 1273-1276 (D.C. Cir. 2010) (collective knowledge inappropriate to prove scienter under False Claims Act); LBS Bank-N.Y., Inc., 757 F. Supp. at 501 n.7 (collective intent inappropriate to show specific intent).
This Massachusetts authority, in turn, also aligns with the weight of Federal authority. Where mere knowledge is required, a plaintiff may show a corporation’s knowledge by aggregating the knowledge of its agents or employees. See, e.g., Kern Oil & Refining Co. v. Tenneco Oil Co., 792 F.2d 1380, 1386-1387 (9th Cir. 1986) (applying Texas law), cert. denied, 480 U.S. 906 (1987); Gutter v. E.I. DuPont de Nemours, 124 F. Supp. 2d 1291, 1309 (S.D. Fla. 2000), citing 3 Fletcher, Fletcher Cyclopedia of the Law of Private Corporations § 790 (1994). See also NM Holdings Co. v. Deloitte & Touche LLP, 622 F.3d 613, 620 (6th Cir. 2010) (applying Michigan law). But where wanton, reckless, or intentional conduct is required, collective knowledge does not suffice. See, e.g., Nordstrom, Inc. v. Chubb & Son, Inc., 54 F.3d 1424, 1435 (9th Cir. 1995); Saba v. Compagnie Nationale Air France, 78 F.3d 664, 670 n.6 (D.C. Cir. 1996).
Pan Am, citing to Bouie v. Columbia, 378 U.S. 347 (1964), and Rogers v. Tennessee, 532 U.S. 451 (2001), argues that the absence of prior Massachusetts law aggregating corporate knowledge in the criminal context means that the judge’s instructions violated Pan Am’s due process rights. Even assuming that the Bouie-Rogers doctrine applies to methods of proof, an issue we need not reach, it applies only to “a judicial construction of a criminal statute [that] is ‘unexpected and indefensible by reference to the law which had been expressed prior to the conduct in issue.’ ” Commonwealth v. Wilkinson, 415 Mass. 402, 407 (1993), quoting from Bouie, 378 U.S. at 354. Because the interpretation we apply has prevailed for decades throughout the Federal courts in the criminal context and in Massachusetts in the civil context, today’s decision is anything but unexpected. Moreover, given the ample sound legal and policy arguments recited in those authorities, so extensive that we will not repeat them here, application of the collective knowledge doctrine to corporate criminal liability is far from indefensible. No due process violation has occurred.
Accordingly, there was also no error in the special verdict slips. We read verdict slips in conjunction with the judge’s instructions to determine whether the slips could have misled or confused the jury. See Commonwealth v. Evans, 42 Mass. App. Ct. 618, 626-627 (1997). Viewing the verdict slips alongside the judge’s comprehensive and accurate instructions, we conclude no such possibility existed here.
The statute provides, in relevant part, “[t]he superior court . . . may *35place on probation in the care of its probation officer any person before it charged with an offense or a crime for such time and upon such conditions as it deems proper ... in any case after a finding or verdict of guilty” (emphasis added). G. L. c. 276, § 87, as appearing in St. 1974, c. 614.
We also find persuasive Federal authority holding that judges have the *36power to place corporate defendants on probation when the relevant authorizing statute refers only to a “defendant.” See, e.g., United States v. Atlantic Richfield Co., 465 F.2d 58, 60-61 (7th Cir. 1972). Prior to the Sentencing Reform Act of 1984, Pub. L. No. 98-473, 98 Stat. 1987 (1984), the relevant Federal probation statute, 18 U.S.C. § 3651, authorized Federal judges to “place the defendant on probation for such period and upon such terms and conditions as the court deems best.” Beginning with Atlantic Richfield Co., Federal judges imposed probation on corporate criminal defendants, reading the probation statute in conformity with the Federal criminal code to include corporations where the statutes used “person” or “defendant.” See Atlantic Richfield Co., 465 F.2d at 60-61; United States v. Interstate Cigar Co., 801 F.2d 555, 556 (1st Cir. 1986) (Breyer, J.) (collecting cases). See also Apex Oil Co. v. United States, 530 F.2d 1291, 1292 (8th Cir.), cert. denied, 429 U.S. 827 (1976). The Sentencing Reform Act of 1984 altered the Federal sentencing statute to permit corporate probation expressly. Pub. L. No. 98-473, tit. II, c. 2, § 212(a)(2), 98 Stat. 1987 (1984) (repealing 18 U.S.C. § 3651 and adding 18 U.S.C. § 3551 [c][1] to authorize probationary sentences for “organizations”).
Because we decide on the grounds that G. L. c. 276, § 87, authorizes Pan *37Am’s probation, we need not decide whether the judge also had the authority to impose probation as part of her discretion enumerated in G. L. c. 21E, § 11, third par. (“The superior court . . . shall have jurisdiction to enjoin violations of, or grant such additional relief as it deems necessary or appropriate to secure compliance with, the provisions of this chapter . . .”), inserted by St. 1983, c. 7, § 5.
The factors are “(1) common ownership; (2) pervasive control; (3) confused intermingling of business assets; (4) thin capitalization; (5) nonobservance of corporate formalities; (6) absence of corporate records; (7) no payment of dividends; (8) insolvency at the time of the litigated transaction; (9) siphoning away of corporation’s funds by dominant shareholder; (10) nonfunctioning of officers and directors; (11) use of the corporation for transactions of the dominant shareholders; and (12) use of the corporation in promoting fraud.” M.C.K., 432 Mass. at 555 & n.19. The court in M.C.K. notably did not consider these factors mandatory; it merely approved of the judge’s use of them to analyze whether the corporate form properly protected the defendants there from derivative liability. See ibid.
These factors included (1) clear intermingling of officers and directors, (2) 100 percent stock ownership of the subsidiary by the parent, (3) parent’s supply of operating funds to the subsidiary, (4) mixture of business operations, (5) the subsidiary’s conducting operations under the parent’s name, and (6) whether the parent derived publicity and good will by representing to the public and its customers that it operated the subsidiary as part of a single entity. Beneficial Fin. Co., 360 Mass. at 291-292.
Pan Am, citing to Commonwealth v. Wentworth, 15 Mass. 188, 191-192 (1818), argues that a different interpretation of “day” may reasonably be applied in criminal statutes. In Wentworth, the court expressly concluded it was “unnecessary now to resolve these questions [of the definition of ‘day’].” 15 Mass. at 192. The court’s nonbinding discussion therefore does not control, and we deem its marginal persuasive value far outweighed by more recent authority, including Booker, 324 Mass. at 266.
As an incentive for settlement and voluntary clean-up, the statute immunizes the settling party from claims for contribution, cost recovery, or equitable share by other potentially liable persons who received notice and the prescribed opportunity for comment.
Although Pan Am argued below that the exclusion of Collins’s statements violated its due process rights, Pan Am does not press this constitutional argument on appeal. Accordingly, we consider only Pan Am’s argument that the judge abused her discretion in excluding this evidence.
This ruling equally affected the Commonwealth. Collins was an agent of Pan Am and authorized to speak about environmental compliance matters on its behalf. Thus, any of his statements made in the course of his agency would be admissible if offered against Pan Am. See Ruszcyk v. Secretary of Pub. Safety, 401 Mass. 418, 420-423 (1988). See also Mass. G. Evid. § 801(d)(2)(D).
For convenience we will refer only to the Fifth Amendment although Collins also invoked art. 12 of the Massachusetts Declaration of Rights.
Pan Am attempted to place the issue before the jury anyway. Pan Am requested a “missing witness” instruction, so as to permit the jury to draw an adverse inference from the Commonwealth’s failure to call Collins. See Commonwealth v. Figueroa, 413 Mass. 193, 198-199 (1992). The judge quite properly declined to give the instruction.
To the extent that Pan Am claims a due process violation flowing from the judge’s decision to deny its motion requesting that she order the Commonwealth to apply for immunity for Collins, suggested obliquely by a footnote in its brief, we do not consider the argument. “Arguments relegated to a footnote do not rise to the level of appellate argument.” Commonwealth v. Lydon, 413 Mass. 309, 317-318 (1992), citing Mass.R.A.P. 16(a)(4), as amended, 367 Mass. 921 (1975).
Pan Am also claims that the Commonwealth’s production of the prior bad acts evidence was untimely. Pan Am argues that this untimely production “compound[ed] the prejudice” of this evidence. To the extent that Pan Am, with this passing and oblique reference, attempts to claim a discovery violation as independent grounds for relief, we do not consider the argument. See Commonwealth v. Nicholson, 56 Mass. App. Ct. 921, 923 (2002) (“The defendant’s passing suggestion . . . does not rise to the level of adequate appellate argument . . .”), citing Mass.R.A.P. 16(a)(4), as amended, 367 Mass. 921 (1975).