The one time I was in a triad, it wasn't 2+1, but a simultaneous joining of 1+1+1. So I'm not sure what other types there are.
But I have wondered about a scenario where I saw someone dating a couple, as if that couple was One Person. Never went out with just one of them at a time....it was kinda odd. I have NO idea what you call that! I just simply joked that the person had a partner who's a set of Siamese Twins, because that's what it seemed to me.