Chrome plating is way out of the amateur's realm. It is a complicated, hazardous process, and not cheap. My father used to work in a shop that did chrome plating (the "hard" type). Mostly the parts would be for hydraulic cylinders and such, but there were decorative parts sometimes, like car wheels, bumpers etc. He was the cylindrical grinding machine operator (oddly the parts were ground before the plating, and afterwards just sanded on lathes for the final "sheen")
It may not be necessary to strip all of the finish off, but the plating will want to stick to all of the surface equally, thus the chrome guys will have to "mask" where you don't want any more chrome to adhere. Part has to be thoroughly clean too (no grease dust etc) or the finish will be impaired. Also any imperfections on the original surface (grinding marks, dings, bumps) will be amplified in the plating process. But I think the best idea is to strip all old chrome first.
Removing the old plating may be possible with some sort of chemical bath instead of abrasion, I don't know for sure.