The simple pushup can be modified by doing them with a partner. I find these are excellent in a class setting, when you've got a number of
Partner Pushups - instead of using a box, you can elevated your feet by using a partner. First get into a pushup position, with your partner at your feet. Then lift up on leg and have your partner hold it, then the other - you'll look like a wheelbarrow (remember wheelbarrow races from Elementary School). From there, do full, normal pushups. These are somewhat easier than a normal foot-elevated pushup because you don't need to push the feet down to keep in position, but harder because you have a vastly less stable "surface" for your feet.
For the partner holding the legs - don't accept sagging, bent legs and forward hips from your pushing-up partner. You are not only the bench, you're the spotter and coach. "Tight legs" and "keep your core tight" have worked for me for cues.
Modifications: Have the holding partner kneel (makes for a lower "box" and reduces the difficulty), change the hand position, add resistance (bands, chains, or a vest), partner alternates holding one leg and releasing the other (increases the difficulty).
Wheelbarrow Walk Pushups - similar to partner pushups, but you walk between each rep. Pushup, take a "step" with one arm, pushup, "step" with the other, pushup, etc. Each pushup will be done with staggered hands as a result of the walking. These are sometimes called "gator" pushups or "gator walk" pushups.
Modifications: Same as above.
I frequently implement these as a competition - total up the reps of each pair for their team total. That allows a relatively weak partner to pair up with a stronger one and have a competitive chance - and their reps count towards victory and may be the margin between winning and losing. I'll try to avoid timed races, though, because that often encourages half-reps and arguments about what should count - more of an issue with young trainees than with adults.