Defendant Gold Medal Bakery, Inc. (Gold Medal), is a large-scale bakery based in Fall River that supplies bread and other baked goods to supermarket chains throughout the northeast. It is a closely-held corporation whose ownership is split evenly between two branches of the LeComte family. The plaintiffs collectively own half of the shares, with the remaining half held by defendant Roland S. LeComte and his sister-in-law Florine LeComte (not a party). Roland S.4 and his son, defendant Brian R. LeComte, manage Gold Medal’s operations. The plaintiffs allege that Roland S. and Brian, together with others, committed a variety of corporate misdeeds. A subset of the defendants sought to compel arbitration of some of the underlying dispute and to stay the entire litigation pending resolution of the arbitration. A Superior Court judge denied their motion, ruling that the agreement under which the defendants had moved for arbitration was no longer of any force and effect. In this interlocutory appeal, see G. L. c. 251, § 18(a) (1), we affirm, albeit on different grounds.
A. Background. 1. Early history. Gold Medal was founded in 1912 by Auguste LeComte. Auguste had two sons, Leonidas (Leo) and Roland A. (father of Roland S.). The plaintiffs trace their ownership interests to that of Leo, while Roland S. and Florine trace theirs to that of Roland A. Joined as a defendant is a second family business known as Bakery Products Corp. (Bakery Products). Bakery Products is involved in the distribution of Gold Medal’s products, and it receives commissions on such sales. From what appears in the record, the management of the two affiliated companies has been intertwined.
2. 1981 succession plans. By 1981, Roland A. had died, and Leo had been running the family businesses. However, at about *236this time, Leo was retiring from overseeing day-to-day operations, and he was succeeded as president of Gold Medal by his nephew Jean LeComte (to whom Florine was married). As is reflected in the minutes of the companies’ meetings, there were extensive discussions about the ownership and control of the businesses going forward. Those discussions came to a head at an annual meeting held on October 27, 1981. At that meeting, the parties agreed that Gold Medal would buy Leo’s shares upon his death, thus resulting in full ownership of that business by Roland A.’s branch of the family. This agreement was memorialized in a written stock purchase agreement (hereinafter, 1981 agreement) that established that the purchase price for Leo’s shares would be paid over a ten-year period (with ten percent down, twenty semiannual payments, and interest set at prime). The 1981 agreement did not, however, establish the purchase price. Instead, the purchase price would be determined by negotiation. In the event that Gold Medal and the legal representative of Leo’s estate could not agree on the value of his shares, the matter would be resolved through binding arbitration. The 1981 agreement stated that it “may be altered, amended, revoked or terminated in whole or in part by a written instrument executed by all the parties hereto.”* ****5,6
3. Rising conflict between two branches. Jean served as president of Gold Medal until his death in 2004, at which time Roland S. took over. Under Roland S.’s tenure, tensions between the branches of the family began to escalate with the anticipated *237buyout of Leo’s branch of the family looming in the background. One of the primary sources of that tension was the fact that Gold Medal sharply reduced payments to Bakery Products, which resulted in decreased distributions to the plaintiffs (who claimed they nevertheless had to pay taxes on the monies retained by Gold Medal). Although Leo remained on the board of directors throughout this period (at least some of the time as chair), the record suggests that he played a somewhat limited role, especially as the decades passed since his retirement as Gold Medal’s president. The plaintiffs played no active role in the management of Gold Medal and Bakery Products, and they began to question whether the companies were being ran in their interests. Accordingly, the plaintiffs made increasing demands for access to information about the companies’ financial picture and the recent decisions by their management. The record does not indicate that the plaintiffs were interested in gaining an active role in operating Gold Medal. Instead, it reveals that they simply wanted to ensure that they were fairly compensated in the impending buyout of their shares.
During this same period, there were active discussions among the various players about having Roland S.’s side of the family buy out those on Leo’s side not only in Gold Medal but in Bakery Products and two related entities as well. The initial discussions contemplated doing this through an amendment to the 1981 agreement, and the plaintiffs communicated their desire to pursue that course of action at a shareholders meeting held at their request on August 21, 2007. The meeting minutes reflect that “[n]o further action was taken on this matter.” Instead, the meeting participants focused on allowing the plaintiffs to have access to Gold Medal’s records so that they could conduct their own audit. The board formally approved that plan.
4. 2007 litigation. Implementation of the agreement to open the companies’ books did not go smoothly, and in December of 2007, plaintiffs Michele and Georgette — together with Leo — filed an action alleging that they were being denied reasonable access. The following month, the parties entered into settlement negotiations, and the record includes many of their written communications. As reflected in a January 9, 2008, electronic mail message (e-mail) from their attorney, Steven E. Snow, *238Michele, Georgette, and Leo initially proposed to enter into a purchase and sales agreement through which they would cash out their interests in both Gold Medal and Bakery Products. Under this proposal, the purchase price was to be “determined by a highly qualified appraisal firm to be jointly agreed upon by the parties.” The new agreement would “replace and supersede the existing [1981] agreement.” Snow’s e-mail concluded by stating that there “will be no binding agreement unless and until the parties execute the [proposed purchase and sale agreement].”
According to an affidavit submitted by their counsel, Anthony A. Froio, Gold Medal and Bakery Products rejected the proposal. Specifically, Froio averred that he told Snow on January 23, 2008, “that the Companies would not entertain any global buy-back proposal that was inconsistent with the financial terms of the 1981 . . . Agreement.” In his own affidavit recounting the progression of the negotiations, Snow does not deny that Froio made this statement.
When the parties resumed their negotiations later that spring, the form of the deal had evolved considerably. Gone was the proposed purchase and sale agreement, or any other new proposal to bind the companies (or individuals) to buy out Leo’s branch of the family. In lieu of pursuing such a proposal, the parties focused on the procedural approach of allowing Michele, Georgette, and Leo to conduct their own independent audit. Thus, the trajectory of the 2008 negotiations largely repeated what had occurred at the August 21,2007, meeting: Michele, Georgette, and Leo initially proposed a new substantive buyout agreement, but the discussions turned instead to trying to satisfy their interests through an agreement to open up the company books.
At least in the record before us, the new proposed agreement first was memorialized in writing in an e-mail that Snow sent to Froio on May 28, 2008. The parties proceeded to trade several iterations of a so-called “term sheet” designed to reflect the essential terms of such an agreement, and they agreed and signed a final version of the term sheet on June 5, 2008. None of the versions of the term sheet mentions the 1981 agreement; from all that appears in the communications between the two sides, Michele, Georgette, and Leo had dropped their insistence that the 1981 agreement be replaced.
*239The final settlement term sheet spelled out the process through which Michele, Georgette, and Leo would conduct the contemplated audit, which was denominated the “Vitale” audit (by reference to the name of the accounting firm that would conduct it). The express purpose of the Vitale audit was “to ultimately lead to the valuation and sale of the Plaintiffs’ shares of the Defendant corporations, to the Defendant corporations and/or their then-remaining shareholders.” Moreover, under the terms of the final settlement term sheet, “[p]romptly after the completion of the Vitale Audit, Plaintiffs and Defendants shall enter into good faith negotiations for such sale.”
Through their counsel, the parties then entered into negotiations over the drafting of a full agreement. Given that the avowed purpose of the final settlement term sheet had been to set forth the essential terms of the parties’ agreement, the final version of the agreement unsurprisingly incorporated the terms of the final settlement term sheet (including the just-quoted language) almost verbatim. At one point during the negotiations, Snow objected to a confidentiality provision that Froio had requested be included. Snow pointed out that this provision was not included in the proposed settlement term sheet, and that, in any event, such a provision “is unnecessary and inappropriate in the context of this case.” With regard to the latter point, he stated: “This settlement does not involve an exchange of money — and it accomplishes nothing other than giving access to corporate records to the owners of 50% of the shares of the companies.” After the parties reached final agreement on the wording of the document, they executed the agreement on July 7, 2008 (hereinafter, 2008 agreement), and Michele, Georgette, and Leo dismissed their litigation seeking access. The executed version of the 2008 agreement includes an integration clause that states in pertinent part as follows:
“This Agreement constitutes the entire agreement between the Parties and supersedes all prior and contemporaneous oral and written agreements, understandings or discussions. Each party hereto has participated in the negotiation and drafting of this Agreement and the Exhibits attached hereto, with the assistance of competent counsel. This Agreement may be modified only by a written agreement signed by *240both Parties reciting the specific intent to modify this Agreement.”
Throughout this period, Leo was alive, living in a nursing home. In fact, he was a signatory to the 2008 agreement (albeit through Michele, who had been appointed his “attorney in fact”). Froio had requested language in the 2008 agreement that Leo was “infirm and incompetent.” In rejecting that language, Snow stated that “Leo’s medical condition is variable,” and that, in any event, his specific condition was “irrelevant because Michele is acting under a Durable Power of Attorney granted when Leo was competent.” None of the obligations set forth in the 2008 agreement was made contingent on Leo’s remaining alive.
5. 2009 litigation. Notwithstanding the 2008 settlement, the relationship between the two sets of shareholders deteriorated once more, with the plaintiffs again alleging that Roland S. and Brian were thwarting the plaintiffs’ efforts to conduct their own audit. This led to the filing of the current litigation on April 3, 2009, in which the plaintiffs in part are pursuing additional information about the companies of which they own half. They seek that information through enforcing the 2008 agreement and their statutory rights to inspection, and through requesting a formal accounting. In addition, based on the information they already had obtained, the plaintiffs allege that Roland S. and Brian, aided by their accountants at an outside firm, engaged in self-dealing, diversion of corporate opportunities, and a wide variety of other corporate misdeeds. The plaintiffs claim that Roland S. and Brian “have used their effective control of the Companies unlawfully for personal gain to the detriment of the Companies and the exclusion of Plaintiffs, and then attempted to conceal their misdeeds . . . through obstruction and secrecy.” The plaintiffs purported to bring their claims both directly and derivatively on behalf of Gold Medal and Bakery Products.
6. Invocation of 1981 agreement. At the time the current litigation was filed, Leo was still alive. He died on April 29, 2010, and his death prompted Roland S. to write to the plaintiffs — in his capacity as president of Gold Medal — seeking to invoke the terms of the 1981 agreement.7 After the plaintiffs *241stated their view that the 1981 agreement was superseded by the 2008 agreement, Gold Medal, Bakery Products, Roland S., and Brian filed a motion to compel arbitration and to stay the litigation.8 In a detailed and thoughtful opinion, the motion judge agreed with the plaintiffs that the 2008 agreement superseded the 1981 agreement. She principally relied on the express language in the integration provision that the 2008 agreement “supersedes all prior and contemporaneous oral and written agreements, understandings or discussions.” She also concluded that even apart from that language, the 2008 agreement implicitly would have superseded the earlier one because the two agreements involved the same parties, covered the same ground, and contained inconsistent provisions. Having concluded that the 1981 agreement was no longer in effect, the judge declined to order any of the dispute to arbitration and to stay the litigation in the interim. The defendants then filed this interlocutory appeal.
B. Discussion. 1. Standing. The plaintiffs argue that only Gold Medal has standing to enforce the 1981 agreement. Because the plaintiffs do not challenge Gold Medal’s standing, it makes no practical difference whether any other party also has standing. We therefore need not resolve this question.9
2. Standard of review. Where, as here, a party has moved to compel arbitration and the other side “denies the existence of the agreement to arbitrate, the court shall proceed summarily to the determination of the issue so raised and shall, if it finds for the applicant, order arbitration; otherwise, the application shall be denied.” G. L. c. 251, § 2(a), inserted by St. 1960, c. 374, § 1. Such motions are treated akin to motions for partial summary judgment, and appellate review is de novo.10 See, e.g., *242Miller v. Cotter, 448 Mass. 671, 676 (2007); Joulé, Inc. v. Simmons, 459 Mass. 88, 92 (2011).
3. Whether 2008 agreement is fully integrated. As the motion judge recognized, the continued vitality of the 1981 agreement depends upon whether the 2008 agreement was intended as a complete integration of the parties’ understanding regarding the sale of Leo’s shares in Gold Medal.11 “A fully integrated agreement is a statement which the parties have adopted as a complete and exclusive expression of their agreement.” Starr v. Fordham, 420 Mass. 178, 188 n.8 (1995), citing Restatement (Second) of Contracts § 210(1) (1981). Such an agreement discharges prior agreements to the extent that they are within its scope; evidence of those prior agreements thus is not admissible to vary or to broaden the written terms of the fully integrated agreement. Restatement (Second) of Contracts § 213(2) (1981). See, e.g., Amerada Hess Corp. v. Garabedian, 416 Mass. 149, 155 (1993). By contrast, if a written agreement is only partially integrated (i.e., is intended as a final expression of one or more terms, but not as the complete and exclusive expression of all terms to which the parties agreed), it discharges prior agreements only to the extent that it is inconsistent with them. Restatement (Second) of Contracts § 213(1) (1981). See Regina Grape Prod. Co. v. Supreme Wine Co., 357 Mass. 631, 634 (1970); Grace & Nino, Inc. v. Orlando, 41 Mass. App. Ct. 111, 113 (1996).
Given the breadth of the integration clause in the 2008 agreement, there is some force to the plaintiffs’ argument that the parties intended the 2008 agreement to be fully integrated. However, “[a]s this court’s decisions have made clear, even appar*243ently straightforward contractual language asserting integration will not always compel a conclusion that a writing reflects a complete and integrated agreement.” Green v. Harvard Vanguard Med. Assocs., Inc., 79 Mass. App. Ct. 1, 9 (2011), citing Holmes Realty Trust v. Granite City Storage Co., 25 Mass. App. Ct. 272, 275 (1988). Put differently, although such a clause is evidence of integration (especially where, as here, the language was negotiated at arm’s length between sophisticated parties), it is not conclusive on the question. See USTrust v. Henley & Warren Mgmt., Inc., 40 Mass. App. Ct. 337, 341-342 (1996).12
A close examination of the integration clause reveals some doubt whether the parties intended a fully integrated agreement. Notwithstanding the clause’s sweeping reference to “all prior and contemporaneous oral and written agreements, understandings or discussions,” the plaintiffs hardly could be heard to argue that the 2008 agreement discharged a prior agreement on an entirely unrelated topic. Some limit to the set of “agreements, understandings or discussions” covered by the clause therefore must be discerned. As we recently highlighted, “no form of words is 1 self-interpreting,’ ” Commonwealth v. Garcia, 82 Mass. App. Ct. 239, 245 (2012), quoting from Antonellis v. Northgate Constr. Corp., 362 Mass. 847, 851 (1973), and it is not self-evident that the integration clause was intended to apply to the 1981 agreement.
In addition, as the defendants note, the integration clause states that the 2008 agreement comprises the complete agreement “between the Parties.” That qualifying language presumably was intended to apply as well to the universe of “agreements, understandings or discussions” that the new agreement would supersede. The term “Parties” is defined earlier in the 2008 agreement to include all the parties entering into the agreement, not just the two parties to the 1981 agreement. This allows the integration language to be read as intending to supersede only those “agreements, understandings or discussions” involving the *244complete set of parties. That supports the defendants’ contention that the integration clause was intended only to supersede the interim “agreements, understandings or discussions” generated in the 2008 negotiation (such as the earlier drafts of the agreement and the various drafts of the term sheet), but not a separate agreement between two of the parties that had been executed decades earlier. This interpretation in turn accords with the common understanding of the purpose of including standard integration language in a contract. See Security Watch, Inc. v. Sentinel Sys., Inc., 176 F.3d 369, 372 (6th Cir. 1999) (“the universally understood purpose of [a] boilerplate [integration] clause” is “to preclude the subsequent introduction of evidence of preliminary negotiations or of side agreements”).
Having concluded that the integration clause in the 2008 agreement unambiguously superseded the 1981 agreement, the judge viewed the negotiating history that the defendants offered as improper paroi evidence. However, the case law establishes that before the paroi evidence rule operates, the judge must satisfy herself that the writing is a fully integrated agreement. See Winchester Gables, Inc. v. Host Marriott Corp., 70 Mass. App. Ct. 585, 591 (2007). Here, the defendants raised sufficient doubt about the intended meaning of the integration clause that “the judge should have allowed evidence of the parties’ negotiations and circumstances surrounding the execution of the [2008 agreement] to determine if [it] was an integrated agreement.” Charles River Mort. Co. v. Baptist Home of Mass., Inc., 36 Mass. App. Ct. 277, 279 (1994), citing Antonellis v. Northgate Constr. Corp., 362 Mass. at 849.
The negotiating history detailed supra strongly supports the defendants’ view that the parties never agreed to displace the 1981 agreement in its entirety. The plaintiffs had proposed to replace the 1981 stock purchase agreement with a purchase and sale agreement, but it is undisputed that the defendants never accepted an agreement in that form. Instead, the parties’ discussions turned to procedural approaches to try to close the gap between their positions. As noted supra, according to his affidavit, Froio told the plaintiffs’ counsel (Snow) outright on January 23, 2008, that his clients would not agree to supersede the 1981 agreement, and Snow does not dispute that this was *245said. Even though Snow now insists that his intent to supersede the 1981 agreement never wavered, he has not pointed to any evidence — apart from the aforementioned integration clause — to demonstrate that vitiation of the 1981 agreement was put back on the table. As Justice Holmes said more than one century ago, a party’s “private understanding or intent” regarding the meaning of a contract is “immaterial.” Equitable Marine Ins. Co. v. Adams, 173 Mass. 436, 438 (1899). See Beatty v. NP Corp., 31 Mass. App. Ct. 606, 612 (1991) (parties’ “subjective and unexpressed expectations” are not relevant in determining the meaning of a contract; “contracts rest on objectively expressed manifestations of intent”). Given that whether the 1981 agreement survived was such a prominent issue for both sides, its exclusion from the agreed-to term sheet (the interim document intended to summarize the key substantive terms to which the parties agreed) is telling. See Wang Labs., Inc. v. Docktor Pet Centers, Inc., 12 Mass. App. Ct. 213, 220 (1981) (“the failure of the lease agreement to discuss expressly . . . two matters apparently of special concern to [the defendant]” suggested that the lease was not intended to “express the parties’ whole agreement”). Furthermore, both parties viewed this stage of the negotiations simply as putting their agreement in enforceable form, not as changing the substantive terms of the deal. And it was precisely during this drafting process that Snow assured Froio that their agreement “accomplishes nothing other than giving access to corporate records to the owners of 50% of the shares of the companies.”
The defendants’ contention that the 2008 agreement was not intended to fully discharge the plaintiffs from their obligations under the 1981 agreement also comports with common sense. The defendants plainly viewed the continued existence of the 1981 agreement as lying in their favor. Among other potential benefits that it provided, the 1981 agreement armed them with a mechanism through which they unilaterally could terminate the plaintiffs’ ownership interest in Gold Medal. It is implausible that they would have given up that mechanism in favor of one that threatened indefinite gridlock unless they received something significant in return. See Schaer v. Brandeis Univ., 432 Mass. 474, 478 (2000) (contracts to be interpreted according to “the *246standard of ‘reasonable expectation — what meaning the party making the manifestation . . . should reasonably expect the other party to give it’ ”), quoting from Cloud v. Trustees of Boston Univ., 720 F.2d 721, 724 (1st Cir. 1983). The plaintiffs have not identified what commensurate benefit the defendants received, or any other convincing reason why the defendants would give up whatever leverage the 1981 agreement provided merely to settle a suit over access to company records.13
An additional factor strongly supports the conclusion that the 1981 agreement was intended to survive as an agreement collateral to the 2008 agreement: each agreement rests on separate consideration. In the 1981 agreement, the two parties agreed to a sale of Leo’s shares on certain terms. In the 2008 agreement, the plaintiffs agreed to settle the 2007 litigation in exchange for certain specifically defined access to the companies’ records. As discussed infra, the 2008 agreement does not create an obligation on the plaintiffs to sell, or on the defendants to buy, the plaintiffs’ shares. The existence of separate consideration for a prior agreement is strong evidence that a subsequent agreement was intended only as a partial integration of the parties’ understanding. See Brennan v. Carvel Corp., 929 F.2d 801, 808 (1st Cir. 1991) (applying Massachusetts law). See generally 6 Linzer, Corbin on Contracts § 25.9[A] (rev. ed. 2010).
For all of these reasons, we conclude that the integration clause cannot reasonably be seen as having been intended to resurrect a key substantive provision (dissolution of the 1981 agreement) that the defendants had rejected. The parties did not agree to displace the 1981 agreement in its entirety, and the 2008 agreement is only a partial integration of the parties’ full understanding regarding the sale of Leo’s shares in Gold Medal. The 1981 agreement therefore may be considered in discerning the terms of the parties’ over-all understanding. See Wang Labs., Inc. v. Docktor Pet Centers, Inc., 12 Mass. App. Ct. at 220.
*2474. Harmonization of the agreements. Even if the parties did not expressly agree to vitiate the 1981 agreement, its arbitration clause cannot be enforced if doing so would be inconsistent with the 2008 agreement.14 See Grace & Nino, Inc. v. Orlando, 41 Mass. App. Ct. at 113. A determination whether it is possible to harmonize the agreements requires a close examination of the nature of the two contracts.
According to the defendants, the 2008 agreement merely “establishes a process for a potential voluntary sale of the Plaintiffs’ shares in both Gold Medal and Bakery Products prior to Leo’s death.” The defendants claim that their obligations under that agreement were extinguished upon Leo’s death, leaving only the 1981 agreement in place. We agree with the motion judge that this reading of the 2008 agreement is untenable as a matter of law. As noted, the 2008 agreement does not in any respect condition the defendants’ obligations on Leo’s being alive.15 Therefore, Leo’s death did not relieve the defendants from cooperating with the Vitale audit or from engaging in good faith negotiations regarding the purchase of the plaintiffs’ shares after the conclusion of the Vitale audit.
However, the plaintiffs’ characterization of the 2008 agreement is also inaccurate. Focusing on the defendants’ agreement to negotiate a sales price in good faith, the plaintiffs portray the 2008 agreement as providing for a comprehensive buyout of their shares. But this ignores the fact that a mere commitment to negotiate in good faith is of limited enforceability. Even if such an agreement were deemed to have some incremental force beyond a mere agreement to agree,16 it ultimately would be unenforceable if either party credibly could claim that a *248good faith dispute remained.17 Thus, the plaintiffs are incorrect in arguing that the 2008 agreement comprehensively addressed the sale of their shares. Instead, consistent with their counsel’s own contemporaneous portrayal of the document, its only substantive “bite” was to provide the plaintiffs with access to corporate information so that they could perform their own audit.
In sum, the over-all function that the parties intended for the 2008 agreement is clear: the parties agreed to have the Vitale audit go forward in the hope that it would allay the plaintiffs’ concerns about potential corporate malfeasance and bring the parties’ respective views of the value of the companies close enough to allow for a negotiated sale of the plaintiffs’ fifty-percent interest. Thus, the 2008 agreement was intended to serve an important but limited role.
Given this understanding of the intended scope and purpose of the 2008 agreement, we conclude that the 1981 agreement and the 2008 agreement are not incompatible with one another. Although both generally dealt with the valuation and the disposition of the plaintiffs’ shares in Gold Medal, the earlier agreement covered some terrain that the later agreement did not, most importantly, what would happen in the event that the parties could not agree on the value of the plaintiffs’ shares. While the 1981 agreement included an arbitration provision, this was a last resort measure that came into play only if the parties could not reach an agreement. The 2008 agreement added various procedures that the parties agreed to undertake before exhausting their efforts to reach a negotiated agreement, but there is no incompatibility between that detail and the 1981 agreement.18 Nor is there any conflict between the audit process envisioned *249by the 2008 agreement and the idea that the parties would go to binding arbitration if their efforts to reach a negotiated agreement after the completion of the audit ultimately failed (a contingency that the 2008 agreement did not purport to address). The arbitration clause in the 1981 agreement is not inconsistent with the 2008 agreement, and therefore remains in force.
5. Motion to compel arbitration. Our conclusion that the arbitration clause is still valid does not mean that the judge erred in denying the defendants’ motion to compel arbitration. As noted, Leo’s death did not vitiate the defendants’ commitment to cooperate with the Vitale audit. The only way to harmonize the 1981 agreement and the 2008 agreement is to conclude that the Vitale audit must be completed, and the parties given a reasonable opportunity to negotiate a sale of the plaintiffs’ shares, before the obligation to arbitrate is triggered.19 While there appears to be a dispute over the extent to which the defendants fulfilled their obligations under the 2008 agreement, the key point for present purposes is that that dispute remains active. Resort to arbitration plainly would be premature until there has been a judicial resolution whether the defendants have satisfied those obligations.20 Therefore, the judge was correct to deny the defendants’ motion.
We acknowledge that our resolution of this interlocutory appeal leaves a host of important issues unresolved. In particular, we have not resolved the related issues what the scope of any arbitration would be, how much substantive overlap there would be between that arbitration and the current litigation, and the *250extent to which that litigation should be stayed pending a resolution of the arbitration.21 The motion judge had no occasion to consider these issues, because she concluded that the 1981 agreement had been superseded. Nor have the parties adequately developed these issues in their appellate briefs. Moreover, resolution of these questions implicates critical case management concerns best left to the trial court judge. To the extent that the defendants have sought a stay of matters that would not be arbitrated, there is serious doubt whether we even would have jurisdiction to consider such issues in this appeal.22
C. Conclusion. Although we disagree with the motion judge’s conclusion that the 1981 agreement was superseded by the 2008 agreement, we conclude that the motion to compel arbitration and for a stay was premature, and we therefore affirm her order denying that motion.23
So ordered.
We use first names and middle initials when appropriate for sake of clarity.
The 1981 agreement did not apply to Leo’s shares of Bakery Products. The record reflects that by the time the parties entered into the 1981 agreement, the parties separately had agreed that an option to buy Bakery Products would be held by one David LeComte (a relative on Leo’s side of the family). The 1981 agreement for Gold Medal stock recognized various contingencies related to David and the uncertain role he would play in Gold Medal’s management. Under various scenarios, Leo could sell or devise all or part of his Gold Medal shares to David, with such shares then excluded from the 1981 agreement. Apparently those contingencies never came to pass, because — despite David’s prominent mention in the 1981 agreement — neither side references him in the briefs.
After the 1981 agreement was executed, Leo began to distribute his shares in Gold Medal to three family trusts as part of his estate planning efforts. The plaintiffs serve as trustees of those trusts, and it appears that two plaintiffs also received additional shares from Leo upon his eventual death. The parties agree that all of Leo’s original shares still are subject to the 1981 agreement to the extent it remains in effect.
Under the 1981 agreement, either Gold Medal or the legal representative *241of Leo’s estate “may invoke this provision by written notice to the other within two (2) months after the date of [Leo’s] death.”
The plaintiffs filed separate litigation in which they sought a declaration that the 2008 agreement superseded the 1981 agreement. They dismissed that litigation after the motion judge agreed with their position in tile current litigation.
We do note, however, that because the ownership of Gold Medal evenly was divided between the two branches of the LeComte family, the agreement by Gold Medal to buy out the plaintiffs meant that the benefits and obligations of doing so necessarily fall on the members of the other branch who were to acquire full ownership (specifically, Roland S. and Florine).
The motion was heard on an agreed statement of facts, supplemented by *242affidavits submitted by both sides. The essential facts are undisputed, and neither party has demonstrated that an evidentiary hearing is necessary or appropriate.
The defendants argue that our analysis whether the parties’ arbitration agreement remains in force should be informed by a “presumption of arbitrability.” Cf. Miller v. Cotter, supra at 680 (agreement to arbitrate not unconscionable, resting in part on the fact that the “purpose of submitting disputes to binding arbitration is heavily favored by statute and by case law”). Contrast Dumais v. American Golf Corp., 299 F.3d 1216, 1220 (10th Cir. 2002) (“The presumption in favor of arbitration is properly applied in interpreting the scope of an arbitration agreement,” and it “disappears when the parties dispute the existence of a valid arbitration agreement”). We do not resolve whether any preference in favor of arbitration applies here, and instead rely on ordinary contract principles.
Accord Marcoux v. Shell Oil Prod. Co., 524 F.3d 33, 43 (1st Cir. 2008), rev’d in part on other grounds sub nom. Mac’s Shell Serv., Inc. v. Shell Oil Prod. Co., 559 U.S. 175 (2010) (under Massachusetts law “a document is not integrated merely because it says so”). See generally Restatement (Second) of Contracts § 209 comment b (1981) (“Written contracts, signed by both parties, may include an explicit declaration that there are no other agreements between the parties, but such a declaration may not be conclusive”).
The plaintiffs emphasize that the 2008 agreement addressed the potential buyout of Bakery Products in addition to Gold Medal. However, the plaintiffs plainly wanted to cash out their interest in the family businesses so long as this was done on fair terms, and all they ultimately agreed to do with respect to Bakery Products was to engage in good faith negotiations. Therefore, it is far from clear that the mere act of putting the potential sale of Bakery Products on the table provided any significant benefit to the defendants, or significant detriment to the plaintiffs.
Both parties to the 1981 agreement were parties to the 2008 agreement, and the fact that the latter agreement included additional parties would not prevent the former agreement from being rendered unenforceable. Roddy & McNulty Ins. Agency, Inc. v. A.A. Proctor & Co., 16 Mass. App. Ct. 525, 536 (1983).
Moreover, as the plaintiffs point out, given that Leo was already in a nursing home while the 2008 agreement was being negotiated, any claim that the defendants always intended their obligations to open the corporate books to evaporate on Leo’s death would implicate whether they had bargained in good faith.
See Lafayette Place Assocs. v. Boston Redev. Authy., 427 Mass. 509, 517 (1998), cert. denied, 525 U.S. 1177 (1999) (“[a]n agreement to reach an *248agreement is a contradiction in terms and imposes no obligation on the parties thereto”), quoting from Rosenfield v. United States Trust Co., 290 Mass. 210, 217 (1935).
In Schwanbeck v. Federal-Mogul Corp., 31 Mass. App. Ct. 390, 398 (1991), S.C., 412 Mass. 703 (1992), we took the view that “the obligation to proceed in good faith means something less than unremitting efforts to get to ‘yes,’ with the players at all times playing their cards face up.” On further appellate review, the Supreme Judicial Court concluded that it was unnecessary in the circumstances to decide whether an agreement to negotiate in good faith creates any enforceable rights. 412 Mass. at 706.
At oral argument, the plaintiffs suggested that the agreements could not *249be harmonized because the 1981 agreement set forth tight deadlines that could not be met if the Vitale audit had to be completed first. This is incorrect. Although the 1981 agreement does include some time frames for resolution of the arbitration once it begins, it includes no time frame for the commencement of arbitration. Instead, it contemplated that arbitration would commence when the parties had exhausted their efforts to reach a negotiated sale. The 2008 agreement provided that the Vitale audit be completed prior to the parties engaging in good faith negotiations to effect a voluntary sale. There is no conflict.
This resolution is also fair. Although arbitrating without important company information might have put the plaintiffs at a serious disadvantage, the completion of the Vitale audit presumably will tend to correct any such imbalance.
Under the express language of the 2008 agreement, “[a]ny disputes regarding interpretation or breach of the terms of this Agreement shall be resolved in the first instance in the Superior Court of Fall River, Massachusetts.”
Under the 1981 agreement, arbitration was limited to deciding the value of the plaintiffs’ shares in Gold Medal, an issue that the pending litigation does not require us to resolve. However, the defendants take a broad view of what needs to be arbitrated, suggesting that any of the plaintiffs’ claims that directly or indirectly affect the value of Gold Medal (such as their derivative claims) fall within the scope of the arbitration provision. In addition, the defendants acknowledge that they seek to enforce the 1981 agreement in part so that they then can argue that the sale of the plaintiffs’ stock deprives them of the standing necessary to pursue a derivative claim. See Billings v. GTFM, LLC, 449 Mass. 281, 296 (2007). Even under the defendants’ broad view and even if all of the derivative claims were to drop out of the litigation, some of the plaintiffs’ claims indisputably would remain, such as their direct claims alleging that the defendants breached their fiduciary duties.
The cases indicate that litigation to resolve a particular matter ordinarily should be stayed if the parties have agreed to arbitrate their dispute, and they treat a judge’s refusal to grant such a stay as necessarily implicated in an interlocutory appeal of a denial of a motion to compel arbitration. See, e.g., Danvers v. Wexler Constr. Co., 12 Mass. App. Ct. 160, 162 n.3, 166 (1981); Ross v. Health & Retirement Properties Trust, 46 Mass. App. Ct. 82, 87 n.7 (1998). Here, however, some pieces of the current litigation indisputably would not be subject to arbitration even under the broad view of the 1981 agreement proffered by the defendants.
We deny the plaintiffs’ request for appellate attorney’s fees.