Not sure this comes up often enough to even bother worrying about and it's likely that the answer is entirely dependent on reads on the villain but this came up recently and made me wonder about the optimal play.
So in the example - multi-way limped pot, Hero in seat 5 BB checks, seat 7 bets, seat 8 raises, seat 10 re-raises, folds to hero who calls, folds to 8 who calls, 10 says call and insta turns up his hand and seat 8 starts turning up his hand when hero says "WAIT! You have another player in the hand"
It's a 1/3 game, there was like $20 in the pot pre, shove was for $140 and seat 10 has nearly 400 behind and Hero covers.
Seat 10 is a rec who's been playing LAGy and bad but hitting flops. He bought in for 100 and doubled through with 52o when he flopped 2 pair. He's been opening hands like KTo from EP and generally very gambly. I've never seen him before and have only played with him for about 45 minutes.
I'm not sure that the hands matter but in this case hero has flopped trips with an A and seat 10 showed trips with a smaller kicker. Seat 8 declared top pair but I haven't seen his hand.
So what's the play? We obviously want to get the money in but what's the best way to do that? If we leave money behind after the flop we can play perfectly but V knows that we've seen his hand. Pretty much anything we do in a spot like this is going to turn our hand face up for what it is.
Without a good read on V aside from his rec/gambly image do we think he's more likely to call a min-raise and get it in on a blank turn or to call a shove now? Any merit to flatting? There's no flush or straight draws on board and we can't have an overpair given the action pre.
Like basically you want to count up your value hands and balance them with bluffs which can still beat the allin player, that's the GTO answer, then you have to adjust that depending on how you want to try to exploit the opponent. It's hard to give concrete examples without the actual hand though. With trips ace kicker you want to be shoving the turn, although jamming the flop was possibly better.
If he's a rec player I wouldn't overthink it. He's stacking off with 2 pair with 52o so he's stacking off with trips. I wouldn't give him the opportunity to make a good play on the flop though, even though he probably never folds. I call and check the turn. I can't see how he checks back as the other V has announced a Q. There are only two Q left so it's hard for you to have QQ or and bigger 3 that isn't going to chop since there's only one 3 left. He bets turn you call or raise then depending on stacks / sizing. If there's any left then GII on the river assuming the 4 hasn't spiked, by then he's committed.
