Are friends a bad idea for arrangements like these?

Me and my girlfriend have been dipping our toes into a sexual arrangement where I meet other women that she approves of. She doesn't want to take the initiative on looking for girl, and although I'm a clean and taken care of specimen, I'm not a pussy magnet, so this has been on the works for a couple months.

Thing is, she has this girl-friend that, for these past couple months, has also become a friend of mine. The three of us talk a lot about sex, both in a superficial as well as a deeper level (no pun intended). And in a couple of conversations, this friend of ours has showed interest in being part of a threesome, furthermore, she was willing to be part of a threesome with us when I asked at a later time.

My girlfriend, although having a very strong trust on her, has been feeling conflicted with the idea. She feels that the deeper connection she has with her friend would get on the way and make things weird and more emotional. She had an idea of something less personal, and the girl in qiestion being her best friend made it too personal for her it seems. I had the impression that sharing something like this with someone you trust would be a good thing for a first time, especially when the three of us have talked about these sort of stuff quite a lot and are on the same page on all of our expectations. Friendship aside, our interests align.

Me and my girlfriend never sought an outside opinion, but I thought maybe if I could gather some more point of views from more experienced people it would help us decide in either leaving the idea aside or not.