If the squat, deadlift, overhead press, and pull-up are the compound movements, then I would consider the TGU (Turkish Get-up) a SUPER compound movement. Ha! Here are a few reasons why...
This is a full body movement that starts from the ground. Think about this for a second; it takes your whole body to work together to get you up off the floor to a standing position under resistance. Most folks are really surprised by how challenging this can be, including many athletes like bodybuilders, olympic lifters, and powerlifters.
Great shoulder mobility and stability is needed. During the TGU, the load is in the overhead position. Your entire shoulder complex has to be activated to keep the kettlebell as still as possible and dynamically staying perpendicular to the floor.
Your lower body strength must be legit. As you press off the floor in the beginning of the TGU, you must drive through your heels to create power and keep your legs from floundering up into the air. You then require leg strength going into a glute bridge followed by a lunge position.
Need I say more why this should be in your exercise program? The benefits go way beyond this list, so give it a try (without weight first), and experience the super and SUPERIOR benefits of the TGU!