Idk about there in the US, but over here many Muslim men have multiple wives, they get married under muslim law by the muslim judical council, and while only the first marriage is recognized by the state, its all legit and accepted and everything...

Just putting that out there, idk if you'd be interested in seeking out a religion that's pro polyamorous.

If not, well others have suggested finding like minded people who'd be interested in the type of relationship you seek, maybe an open marriage is an option...