If your old grout is cracking, then, technically, new grout can be placed over the old grout, but that is just a temporary solution. In a short time, the cracks come back. The Floor Elf holds that the best, permanent solution is to remove the old grout and start over.
Trying to place new grout over old grout only creates another layer of grout. There’s no true adhesion; the new grout sticks to the sides of the tile rather than the substrate below. The Floor Elf suggests to focus on the original problem. Cracking grout was most likely caused by shifting tiles, which could be due to faulty tiling or movement of the substrate. One example would be if tile was placed on top of plywood. Plywood breathes with humidity, so, over time, it causes shifting of the tile and cracking of the grout.