i've never been a fan of getting AKs all in preflop (cept vs short stacks obv) coz most ppl are very rarely willing to play all in preflop with a range that AKs fairs well against.
Anyways, only two options to me. Fold preflop, or squeeze/call shove. You can't squeeze/fold, because pot odds
are just too good...you can't raise to something like $24 here and expect folds.
Frankly, i've folded this preflop before because i really just don't want to get involved in a situation where my equity is highly unlikely to be very good/the squeeze probably isn't going to work. Vs fishy opponents i'd probably get it in, but vs decent players with a raise/3bet/cold call i don't think you are picking up the pot often with the squeeze and i don't like the flop decision/equity if called and i hate the equity if one or more of them shove preflop. The only thing that would make me think the squeeze might work, is because the 3 bet came from a 26/15, but with such a small hand sample you can't have much of an idea of his 3 bet range. Suggesting folding preflop might seem quite odd, but oop with a raise/3 bet/cold call is not a situation i think you ever want to be in with AKs unless you are vs fishy players. I really try to advoid shitty positions like this, even if it means i have to lay down a good hand.
EDIT: Well actually i guess squeeze/fold is an option, because with all the all ins your equity is probably complete garbage, but that just seems like a huge spewy leak to me.
Let's say that the $31 raise was the right amount. There is ~$20 in the pot you can win from the squeeze, so it has to work 3/5 times to break even. If called, you are in big trouble when you miss being oop, and either have to c/f or quite potentially spew more chips hoping villain folds a biggish pp because you "rep" AA by shoving flop. If villain/s shove preflop, you can't really get away from the hand, so have to put in $60 more with likely bad equity, or you find it in yourself to fold and throw away $30.
Squeeze more, and you 100% are committed...squeeze less and you decrease already fairly poor FE.
So all in all, i think it is fine to just advoid this situation altogether vs some opponents. It's simply a bad spot to be in.