I have had the experience when I went all-in against a nice, trailing but improvable 2nd-best hand on the flop. Now I got my money in as the favourite, but is there a way for me to maximize my EV by just calling, assuming that villain will be married to his hand no matter what?

Here are 2 examples, NL25.

Villain had ~60BB, I had him covered. I raised 4x preflop with KK, and my unimaginative donkey villain limp-called in EP, everyone else folded. The flop was KAA, giving me a vulnerable full house. I bet 5x into a 9x pot and was minimum check-raised by villain.

Now it's obvious that he's got an Ace, he really liked his trip Aces, and I was a 77% favourite. In actual play I 3-bet all-in, he called with A4s and paired his rag on the river.

Assuming that villain won't lay down his hand no matter what, would it be even more profitable for me to just call down flop and turn before shoving river unless he obviously improved to a full house (turn and river pairing) or quads? This would allow me to get away and save some money if I was OBVIOUSLY outdrawn (not here, coz I wouldn't recognize the 4 as his out, but I could get away from 4 cards -- the Ace and 3 other cards that would pair the turn -- on the river).

Another example:

I have 64s in BB and called a 3x raise by an LP. A tight-passive nit open limped in MP and called the raise as well.

Flop was 357 raimbow giving me a straight. I led out 6x into a 9x pot and MP raised me big (to 24x), original raisor folded. Since villain was tight passive in general he had to have a set here. I pushed my full stack, he called. He had 77 for top set, and he didn't improve.

As played I got all-in on the flop as a ~67% fav. But was 67% good enough? I knew I could probably get away if the board paired on turn. Is it better to call flop and c/r all-in a non-pairing turn?