How are you going to get beneath the block that you just caved in in order to remove its support to drop it into the next aquifer layer, given that the layer beneath said block is an aquifer layer?
You can use the cave-in method to pierce multi-level aquifers, but it's somewhat more complicated than that. I've done it for a 2-level aquifer and could've used it for a deeper one, but the only time I've embarked on a place with an aquifer more than 2 levels thick it was in stone and there as an incredibly convenient series of non-aquifer large clusters that lead me through the whole mess.
Basically, actually caving in through multiple z-levels of aquifer involves making a series of concentric rings, each detached from the other but supported, then caving in the outermost ring to get through the top aquifer. Then, you remove the material within the caved-in right; there will be water, whether you dug out all of the walls beforehand or not, because since you didn't cave in the inside tiles the aquifer tag wasn't cleared off of them, and even aquifer tiles totally disconnected from all others produce water in limitless amounts. As such, this involves at least one pump. Then, you repeat the process with the next z-level, caving in the next ring, then the next, and so on, until you're caving in the central block that you can actually go through to the other side of the aquifer.