I recently tried to pierce a 3 layer aquifer, and here's what I learned:
Cave-ins require a lot of knowledge to produce proper results with a minimum of damage. The one I tried resulted in the unlucky death of the mason who got picked to initiate the cave-in, along with half of my food stores being entombed in a perpetual deluge of water. Also, I had an issue with a floor of Open Sky caving on to my last surviving miner and entombing his pick in ice. I didn't try to explain that one.
Breaching with pumps is trivial if you have a single layer aquifer, doable with a two layer, and anything above three, don't bother. The triple aquifer embark I had had two non-smoothable aquifer layers, and a final third layer of aquifer stone. The issue arises that with soil layers, you have to construct walls to block the flow of water, and with stone layers you at least don't have to build new walls, you can just smooth, but either way you're stuck reducing the size of your breach. I started with a 7x7 (reduced to 5x5 by walls) on the first soil layer and couldn't muster enough pumping to fix the next level, and then below that, I still had a meager 3x3 space to stop the third aquifer layer, and you can't even reasonably put a pump in there.
You can try draining a higher aquifer layer into a lower aquifer layer to help with managing the outflow. Just note, this is FLOW, and it will shove your dwarves down any trench you dig to try and help eat up the upper aquifer water. My experience was 95% of the time they could eventually escape, but even still I had a casualty or two from flow shoving them down a level where water isn't draining.
My experiences say if your map freezes water at some/all points and you can afford to expose your breach to the outside, go with that. Just note if it's seasonal freezing when to halt all mining and get everyone out of there before they get iced. If your map doesn't freeze... well, mod or outright cheat. Breaching aquifers with pumps, especially triple layer or more, is a years long task. Cave-ins are probably the fastest way but they offer a lot of risk for reward if you don't plan ahead.
Oh yeah. Bring stone. Lots. Cause odds are you won't have any for a while.