I've found that doing push-ups on one knee (the other leg held out behind you) is an intensity between on-the-knees and on-the-toes push-ups. But I now feel that it's better, as others have mentioned, to do push-ups with your body straight and your hands at gradually lower levels. The transiion between these kinds of push-ups and on-the-floor straight leg push-ups would be smoother, IMO.
Start wherever you need to: hands on wall, hands on kitchen counter, hands on edge of bathtub, hands on seat of kitchen chair, hands on step of various heights, until you transition to the floor.
Another method would be to do the push-ups using a stability ball. Start with the ball under your hips, then gradually move the ball closer and closer to your feet as you improve. One advantage of this technique is that it's easier to change intensity in the middle of a set, as the more challenging version (ie: feet on ball) becomes too challenging, and you can quickly move to a less chanllenging version (ie: ball under shins).