I've never been in a threesome that involved another man, but threesomes are best kept to the times when you are not involved with anyone, in my view. So I wouldn't be doing it with my girlfriend.
But *IF* I was in your position and decided to go for it, then it would either have to be with a stranger to both of us or else with someone I knew but she didn't. Worst scenario would be a friend of hers whom you don't know (or don't know well).
But if you choose someone you know, best not be someone you (or your girlfriend) socialize with at present, or all your mates (and perhaps also her friends too) are likely to hear about the time he fucked your woman. The details will probably get embellished in the telling, too!
Anyway, whoever you choose, it had better be someone from out of town and therefore relatively inaccessible, or you might find yourself as number three in the threesome before too long!
Let us know what you decide!