1. Literally, to strike, smash, or crush someone or something with one's foot. I stomped on the hot coals to extinguish them. The group of assailants knocked the poor man down and stomped on him until he was unconscious.

2. By extension, to subdue, suppress, of inhibit someone or something forcibly or without. My father always stomped on my dreams of becoming an actor. The company made a point of stomping on any employee who so much as suggested forming a union.