That idea won't work because it doesn't actually make sense. While it is definitely an interesting question; and one that I was initially puzzled by, I think you will be surprised by how clumsy the intuitive logic that brings us to that conclusion is.
Consider your onion, with two layers, and you are standing between them. To make things simpler, lets assume that instead of water pressure you actually have pressure from weights, and lets also change your onion from spherically shaped shells to just two flat surfaces. For example, you could imagine that you are just standing on an imaginary, levitating sheet of plywood and there is a sheet of plywood above you.
The "water pressure" from above you is say 100 lbs. This is how many weights are on the sheet of plywood above you, and it is as much as you can hold. So you say, lets "pressurize" the intermediate onion layer (you), and you position springs on both sides of you (or you could use water pressure). With this new pressurized layer, you can now withstand twice as much "water pressure" from above you, for a total of 200lbs. But that has nothing to do with how much pressure is being exerted on this imaginary sheet of plywood beneath you.
As you see, you could build a million onion shells and it wouldn't change anything about how much pressure the inner most layer, or the bottom sheet of plywood, must withstand. Indeed, all submarines already use your multiple hull theory, but not in the way you imagine. They all must withstand the pressure from a layer of ocean above them AND a layer of atmosphere above the ocean--the ocean doesn't protect against the atmospheric pressure.