Of all the awkwardest imaginable situations.... I guess if everyone's drunk and it happens, it happens. But to soberly plan that sort of thing out? It seems QUITE impossible to not really piss off at least one of the females, if not ruin some relationships. It seems like a very volatile situation with no clear sexual benefit, but a lot of downsides. Sex is bad enough with one person.
You are going to say "yes, but on one condition! I choose the guy." That is the way around this whole threesome issue. Whichever partner is the same sex as the third person joining in gets to choose who that person is. Girl chooses the girl, guy chooses the guy. This way any insecurities, doubts, or worries that may be involved can be removed. If you're a girl choosing another to join you and your man, you can make sure that you are better looking than her, have bigger breasts, she's completely random and unknown to your man, there's no way for her to contact him after it, or any other worry that you may or may not have. On the other hand if you're a guy choosing the guy who will join you and fuck your girl with you, you can make sure that you're better looking than him, have a larger cock than him, your girl cannot contact him afterwards, and all the rest. You could even tell the guy beforehand that you girl's pussy is off-limits to him (which of course still leaves open the option of anal sex and DP if your girl is into that) if the two of you decide to keep vaginal sex just between yourselves. Of course to get this far though you would both have to be at least bi-curious and willing to try new things.
No clear sexual benefit? If you're a guy, just imagine TWO tongues wriggling up and down your shaft. If you're a girl, just imagine TWO tongues wriggling all over your clit and inside you at the same time. That's just for starters...
Threesomes can be really tough emotionally. I would suggest trying out couple swapping instead. You can start with same room play (with your partners only, but in the same room), girl on girl then the girls only fuck their partners, or do a soft swap where you can fool around with whoever, but p in the v is only with your partner. Then you can progress from there to full swap if you want.
Just imagine banging ONE chick, while ONE crosses her arms and gets all pissy that you can't multi-task...
Who said men can't multi-task? Problem solved! There's countless ways that all three can be involved at once.