Weight wise it is no problem, space-wise it is. PL-15 is thicker than the AIM-120D and has wider fins. Even when stacked there isn't enough space in the main bays for 6 missiles.
Based on the weapons bay images, I think there is lots of room. The issue is that the J-20 isn't really using it effectively. The PL-15 still has some room length wise and stacking it along that way shouldn't be impossible. It's very odd how small the weapons bay is given the size of the aircraft.
Many aircraft like the F-22, SU-57 and the F-35 had less missiles to begin with with future upgrades better utilizing the weapons bay.