So alpha Rey and alpha Poe sharing omega Finn. Maybe Finn was on suppressants in the First Order and this is the first time he's been able to explore this side of himself. Finn has been so deprived of attention having two alphas who love him can be slightly overwhelming at times but mostly its awesome.

Maybe Poe and Finn bond soon after the events of the movie. When Rey comes back she finds that she's still drawn to Finn despite him being bonded to another alpha. However the guys are totally open to letting her join their relationship. She's never been with anyone before and Poe shows her exactly how to take Finn apart. Rey being Rey she's a quick study.

It can play out pretty much any way as long as Finn is an omega with Rey and Poe as alphas.
Whether Poe and Rey have sexual contact is up to the author.

Finn having a boypussy is optional but not necessary.