Over the last few years I've refined my mirror finishing process. To start, some steels will polish to a mirror with relative ease, and others won't at all. 440C, CPM154CM, 1075-1095-1084 all are easy enough to finish, D2 will polish brightly but the grain of the steel is very evident, and CPM 3V and S30V in particular are nearly impossible. Bruce Bump has finished S30V to a mirror and the search function will give you more information on that.
My grit progression is 50g, 100g, 100x (micron), 45x and then 15x. I finish off with a worn 15x belt with white buffing compound applied in the hollow grinds, potentially stepping back to a new 15x belt if I find any stubborn deeper scratches. Then on the blade flats, using the flat platen through the grits to 15x, I go to 400g hand sanding, then 600g, 1200g, and 2000g. I alternate sanding directions between each grit, and the last few grits go surprisingly fast. Buff with white compound on a sisal wheel then green on a softer buff.