Plyometric Push Ups, or jumping push ups, are a great way to scale up the push up movement within the same range of motion by increasing speed and adding explosive power.
Plyometric Push Up Progression Part 1:
How to do a plyo-push up:
In this video, Coach Carl begins by explaining why the jumping push up requires an increase of not only speed and strength, but also skill via motor control as the body loses points of contact in the hands as they leave the ground. Carl then demonstrates the optimal ratio of speed and rhythm of the descend and push up to generate the most tension and power. As you build enough speed and power to take off, Carl addresses the proper hand positions for that extra pop and receiving the landing.
Also check out Plyometric Push Up Progression Part 2.