Ah, yeah, four tanks is a bit of a hassle. I made a burst disk cartridge gun with my idea in reverse. It has three barrels, each leading to a bv, which connect commonly on a three inch endcap, which was the end of the gun.
From there, I would just charge the the gun witha co2 inflator, shoot a cartridge, close the bv on the shot shell, and open the bv for a new one.
Idk, maybe this will give you some sort of idea for a multi-shot design.