Linoleum parfait

[JT Spangler]

So, as I suspected (but hoped I was wrong on), the kitchen/hallway/bathroom/laundry in my new buy and hold property have linoleum on 1/4" plywood underlayment, underneath which is another layer of linoleum, underneath which I assume is the original subfloor.

Initially I was just gonna lay vinyl wood plank on top of it, but I can't just keep stacking flooring on flooring. So I really should pull up everything down to the original subfloor. Anyone have any tips for removing old linoleum on a plywood underlayment like this? Or is it just go to work with the prybar and skilsaw set to the proper depth?