[Nick C]

I would have folded preflop. (I don't like ATs versus a raise very much.) However, MP3 could be trying to isolate MP1, and you are at least suited, so I don't think the call is terrible, from the SB.

Postflop seems all right to me, really. The pot's only 3-way, and if you're ahead, MP1 probably doesn't have much chance of outdrawing you anyway, on that flop, so putting pressure on him doesn't seem all that essential to me. And you're probably either way ahead or way behind MP3.

Checkraising the flop could be a way to try to figure out which it is, but doing so also provides information for MP3. And if, for instance, you checkraise the flop and get called and then get popped on the turn, you've only saved one small bet over just calling down, at the cost of giving up your chance to spike your kicker on the river (which would be worth about one SB at the moment when you'd be folding).

If your checkraise gets 3-bet, then that could save you money if you then check-fold the turn unimproved. But MP3 won't necessarily cooperate like this. And while I don't think your opponent will 3-bet with a hand like QQ and then fire again on the turn particularly often, it will happen occasionally and will cost you money when it does.