You can't do small joint manipulations. What that means is it is illegal to grab fingers or toes and bend them intentionally. You can break your opponents fingers unintentionally or intentionally by kicking or punching their hands, but it's not an effective technique.
The Ultimate Fighting Championship allows stomps to be performed from the clinch, while stomping on a downed opponent is considered illegal. Although now defunct as a promotion, PRIDE FC rules allowed competitors to stomp on a downed opponent, either to the head or body.