I can only say that playing around (with yourself) - trying to have your cake and eat it do - is pretty frequently an exercise in frustration and failure.
you have to be 'true' to who you are as much as possible to maintain your own health & happiness. If you are truly bisexual, and truly drawn to multiple loving relationships, then trying to maintain one with someone NOT on this page is going to be difficult.
You would be (potentially) asking them to change who THEY are to satisfy you. Won't happen - or shouldn't at least.
One of the things about opening our hearts to poly loving is that along with that comes the requirement to love and move on in cases where conflict would actually undermine that love.
Does that make any sense ? Hard choices I know, but life is full of those.