A high rep training method that I’ll use from time to time is referred to as as extended sets or mechanical advantage sets. Basically you’re starting from your hardest angle of work and moving to angles where you’ll gain more of an advantage because the force being applied is less. For instance, you could start with a dumbbell incline press, go to near failure and then move to a flat dumbbell press. Or with push ups you could move from a foot elevated position to a position where your feet are on the floor to a position where your hands are elevated.
In the following video, I take use this same principle of mechanical advantage with push ups on the TRX®. I start from the hardest angle which is near parallel to the floor. As I get to near failure, I walk my feet up a bit so that I’m slightly angled to the floor and go to near failure there. And then I finish off the set by walking my feet a couple more inches forward and squeezing out a couple more reps.