Does anyone have experience w/ removing multi layers of paint from a car?

I'm re-painting my IT car which has been painted (whole car) at least twice previously, beyond its OEM paint. The surface in many places has little "mud cracks" in it because the stuff underneath is so thick.

A single edge razor takes off the first layer pretty readily, but the sealer underneath that, then the previous coat(s) and their sealers are pretty well adheared. The OEM first primer (to metal) is in good shape, but getting the stuff on top of it creates lots of nicks.

Any chemical strippers that will help soften up the top layers? Or do I just buy a case of single edge razors & a case of 50 grit paper for the DA?