Sliding Side-to-Side Push Up
You can use two paper plate on carpet to platform the sliding side-to-side push-up. (Also you could use commercially-available sliding exercise discs or, on a slick floor, small hand towels.) This is a highly challenging shoulder and core movement. Alternate hands, performing a push-up with one arm while sliding the other hand up in front of the body. Control the core and prevent excessive shifting and twisting.