No. That's why we have the third party app. And why do you need group pm? For group rp? On second thoughts, group rp doesn't sound bad ?
Are they not called clubs or tutor chat? I imagine the lag if people could make tons of groups here. It would kinda be like mini clubs.
Campus chat, club chat, private chat...I'm hoping that by now you've reevaluated your idea and realised it is like a boat full of holes :|