I agree with NR, this could be really dicey. If I were your bf I wouldn't want to move in with someone I'd just started seeing anyway, poly or no. What if it doesn't work out between the two of them and there are hurt feelings? Then all three of you guys would either have to suck it up and deal with a painful living situation or you two would be without a place to stay. The latter scenario is especially worrying since it sounds like finding a place you can afford is difficult. Or even worse in a way, what if he keeps seeing her even though it's not working out for him just because he feels like he has no other choice, to preserve the living situation? It'd be different if he and she had been together longer and knew what they were after from each other.
It *could* work out, sure, but I'd hold off.
Me, 30ish bi female, been doing solo poly for roughly 5 years. Gia, Clay, and Pike, my partners. Davis, ex/friend/"it's complicated." Eric, Gia's husband. Bee, Gia and Eric's toddler.