The facts giving rise to this case are familiar to the parties and reported in the district court's order. So a simple CliffNotes summary suffices for purposes of this opinion-an opinion that is a companion to our decision released today, Britto v. Prospect Chartercare, LLC, --- F.3d ----, 2018 WL 6257007 (1st Cir. 2018) [No. 18-1422], knowledge of which is assumed.
Plaintiff sued Defendants in federal court, basically alleging that they fired him in violation of the Family Medical Leave Act and the Rhode Island Parental and Family Medical Leave Act. Defendants later asked the district court to dismiss the case and compel arbitration based on the parties' signed arbitration agreement. Concluding, however, that the agreement failed for lack of consideration, the court denied the motion.
According to the district court, the parties' mutual promise to arbitrate constituted insufficient consideration to support the arbitration agreement, because Defendants reserved the right in an offer letter to change Plaintiff's employment terms, like submitting disputes to arbitration, at any time-circumstances, the court said, that made Defendants' promise to arbitrate illusory. The district court also concluded that Defendants' offer to keep Plaintiff on as an at-will employee, made at the time of the agreement's signing, constituted insufficient consideration as well-a conclusion, the court added, driven by a Rhode Island trial court opinion, D. Miguel & Son Co. v. Barbosa, No. C.A. 84-3186, 1985 WL 663146 (R.I. Super. Ct. Mar. 11, 1985).1
Defendants now appeal. And we review de novo . See, e.g., Nat'l Fed'n of the Blind v. Container Store, Inc., 904 F.3d 70, 78 (1st Cir. 2018). Without deciding whether Defendants' rights reservation made their arbitration promise illusory and thus inadequate consideration, we hold that their offer of continued at-will employment is valid consideration for the agreement, given a Rhode Island Supreme Court opinion, Oken v. Nat'l Chain Co., 424 A.2d 234 (R.I. 1981) -a holding compelled by our Britto decision, 909 F.3d at 513-14. Just as it did for the Britto plaintiff, *518Oken rejects the very arguments Plaintiff briefed to us here. And there is no reason to repeat in these pages what we wrote in Britto.2
A couple of loose ends remain to be tied up, however, and we are done.
First, Plaintiff moved in this court to supplement the record with pages from an employee handbook that he says "reinforces" his and the district court's view that Defendants "retained the right to change the terms and conditions of [his] employment at any time, including the [a]rbitration [a]greement." Because consideration of the handbook would make no difference to the result we just reached, we deny the motion. See Riley v. Rivers, 710 F. App'x 503, 504 (2d Cir. 2018) (summary order).
Second, in the conclusion section of his brief, Plaintiff suggests for the first time that the arbitration agreement is "procedural[ly] unconscionabl[e]" and therefore unenforceable because of the circumstances surrounding the agreement's signing, at least as he "recalls" the circumstances. And he asks us to remand "for limited discovery" so he can flesh out his recollection, which would then allow the district court to resolve "the issue of procedural unconscionability." Not only does he fail to give us a legal basis for how we can order discovery in the circumstances of this case, he also does not explain how-in addition to being procedurally unconscionable-the agreement is substantively unconscionable. See Britto, 909 F.3d at 515 (noting that Rhode Island law holds "a contract is unenforceable if it is both procedurally and substantively unconscionable"). And so we deem the argument waived. See Town of Norwood v. Fed. Energy Regulatory Comm'n, 202 F.3d 392, 405 (1st Cir. 2000) (stressing that "developing a sustained argument out of ... legal precedents" is a litigant's job, not ours); see also Muñiz v. Rovira, 373 F.3d 1, 8 (1st Cir. 2004) (emphasizing that a party waives an argument by presenting it "to us in skeletal form, without citation to any pertinent authority").
The bottom line: We deny Plaintiff's motion to supplement, reverse the decision of the district court, and remand the case with instructions to grant Defendants' motion to dismiss and compel arbitration. Costs to Defendants. See Fed. R. App. P. 39(a)(3).