Striking in the Demilitarized Zone (*GASP!* From Side Mount!)
If you haven't seen it, watch it, strictly for its excellent example of total domination via the technique I'm describing.
I like to move to the high side mount, pin one arm with a knee, the other with an arm, elbow the face. It's my favourite position to strike from...lets you isolate their face so badly, and dish out shot after unanswered shot. Obviously, it's harder from the bottom, but do-able.
You can also go to knee-on-belly and do it, but it's a little less stable that way.
You can do it from the bottom the same way; move out to the side and strike from guard, instead of going for the back. I don't see too many people do it effectively, but once you're on one side, it's your two arms vs their one. If you're always hitting, hitting, hitting, you give yourself way more chances to go for subs and get to better position.
Hold his near arm with one of yours and hold his other arm away with a leg and bash him with an elbow, fist, or palm. You've got the triangle, the omoplata, the armbar, and the elbow-to-the-face all right there, once you're off to the side, and you still don't give up your chance to go for his back if that's what you have your heart set on.
It throws people off if you strike them when they're expecting a sub attempt/reversal/other grappling manuever. Strike, strike, strike. The only time you should not be striking in MMA is when you're not in range, blocking strikes, or you absolutely must concentrate all your limbs on a grappling technique to make it work. This is a slight (but only slight) exagerration, you get the idea.