No worries about the tangent, this is a subject that interests me.
So, ok, let's say you and your gf start dating someone together. That person gets way into your gf (maybe not love, let's say strong like) and she's way into the new person right back, but rather than you and the new person getting closer, you find you really don't click after the excitement of the first few dates wears off. You two actually come to realize that while you don't have a problem with each other you don't even really like hanging out all that much and you're not feeling the sex. So now it's not just a matter of unequal feelings, it's actually just your gf dating someone without your involvement, it's a vee.
Do you insist they break it off? Or is it cool? And what if the shoe were on the other foot, same scenario but roles reversed -- what do you think your gf would do? If you can honestly say it would be fine, then sure, go ahead and seek a person you both like with that lack of expectations firmly in mind.
Finally, I think this simple question is really important -- *why* do you and your gf think dating the same person is the best arrangement for you? To prevent jealousy? It would be good for you to be aware that it actually seems to tend to be more likely to foster it, since it's more difficult to avoid comparisons when everyone is in the same space together all the time. Or is there another reason you think it would be best?
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.