How can I animate multiple body parts simultaneously from 2D sprite sheets?

Right now I currently have multiple game objects with separate animators parented to a game object with the animation script. It works fine, but I'm wondering if I can combine my game objects into one so that I can use separate 2D sprite sheets to animate different body parts?

I'm eyeing layers for this, but I cannot figure out how to play multiple layers at the same time. Maybe I can't, but then what is my next step here?

Thanks!