Don't worry about offending people on this board! It's all good. Asking should always be safe. Coming out (even anonymously) is really hard. Congrats on speaking up. I know it took me years to speak up (even under a pseudonym) about what I was living.
I think the name for what you're describing, in the kink world, is being a cuckquean (the female version of a cuckold, I guess).
For this... I don't know, maybe you can talk to your boyfriend into doing this with him, and that part of the "game" is that you bring home the partners. That's more for the sexual side, and not the relationship side. From the relationship side, I dunno, that's a complicated dynamic, but one I'm sure can be found or created over time.
Because your boyfriend knows what you're wishing for, maybe he can help you move forward with it, as well. Help you discover what you want - him in a committed relationship with someone else, and you in a relationship with her, as well, but you no longer in a sexual relationship with him? You occasionally bringing home someone you serve, while she is with him? The details might really matter, but as long as you two are walking this path together, and know what you seek (and know what seems impossible to find, etc.), then I think you might just find what you're looking for!