As played I have to call off unless I am literally certain he only has QQ+. I need ~22% equity to call, which is easily achieved once you throw in a combo or two of AKs.
I do agree with Amana that keeping the loose passive player in the pot is good. And, even if I am correct that villain has a lot of AK, 4bet/calling still is only slightly winning.
But flatting and playing JJ OOP in a multiway bloated pot isn't much fun either. Unless the flop has a J
Gross spot. I lean slightly towards Amana but still need to think about this one.