I play the flop differently. I check hoping to raise MP2, but with the raise from CO, I just call, planning to cap a 3-bet from MP2. You can not buy outs or protect your hand.

I play the turn the same. I don't think you can buy any outs on the Turn. I think a river 2-pair is rarely good given the action and board so far.

I bet out on the river. I don't like check/raise because it may get checked through.

Hand Reading:
Without any reads on the players, I have no idea what people are holding, but here's my best guess.
After the flop, you can put MP2 on AK, AQ, AJ, or AA. After the turn, I think AA is very unlikely.

I put CO on AK, AQ or 44, 77. But if he is very loose preflop, you can include A4 and A7.

BB and MP3, who knows. could be any number of draws including flush draw, straight draw, or a draw to pair. I think a slow-played set is unlikely but possible.