Yeah, "surprise threesomes" do sound like quite weird. I mean for it to come totally out of the blue would be a bit strange. Don't get me wrong, if that's like what you enjoy, then great, but, it doesn't really do much for me.
And to be honest, the choice in the relationship I'm in would be between H&T (the two people who have put me on the 'straight and narrow') and if they wanted to do it. I mean T is H's long term male partner and I can't imagine H wanting another man especially as she seems like very happy at the moment.