PLO10 AQQ3, quads in 4way pot

I would not check-back the turn. I know slowplay is good as we give em the possibility to improve but they are likely weak/loose so I would bet small to build the pot a little bit more for a bigger river sizing. I mean, the KJJ9 will stick around anyways if he's bad and you bet like 1/3 pot so the river 2/3 pot-size bet will be a little bigger and we get more value, any prob calls anyways aswell.

i disagree with betting turn small. if you think about what people hold here you will be seeing mainly OPs and a miracle underfull. now when 3 players see a turn obv there are trips+ sitting somewhere. generally you will not get more than 2 streets of value here so it doesnt matter vs the weaker overpairs if you bet on turn or river but what really makes me check turn is to see a river with some overpairs that evolve to a boat so we play for an expensive second value street

as hand run out i already see hard times getting a second street value so i would tend to bet small up to 1/2 pot. as OP said it will be hard to get a sedond street of value even from undertrips, even when betting small because we generally cant have bluffs here...

you will not get more than 2 streets of value here

Last time I had quads the hand got played out just like this one and there was a guy who paid off 3 bets (3x 1/2pot) with bare overpair. I had :Qx::Qx:xx and board was :Qx::Qx::Tx::Tx::4x: rainbow too and he showed :Kx::Kx:xx.

The posted hand is multiway so it is more likely someone could hold a hand that he wants to call.
I also think to be betting pot on the river makes sense, cause if he has an underfull or trips top-kicker he is likely to call any sizing once he checks but not so inclined to check-raise if you bet small so you cant reraise. Sometimes if you bet small on the river on the other hand (but not when the board is double paired) you can get more value against weaker fulls when he is raising your small bet for value and they cant fold vs your 3-bet. I mean against top-full it goes in anyways but against more lower fulls you can play it tricky.

But idk. Alltogether I cannot say what's better for sure, you dont get quads very often and the river spot is super-rare..