My girlfriend suggested having a threesome to me, should we do it?

That can be awkward and a slippery path. Make sure to thoroughly discuss whats acceptable and whats out of bounds. Some men are ok with a FMF, but don't want/can't handle MFM. Ask her why, is it with an ex, a friend or someone else? Is this a one time experiment, or does she want to "open" your relationship?

Some men thing "Great! this will show her how amazing I am." Only for her to react more carnally with the other man, maybe do things with him that she won't do with you, or just find out other men are better lovers.