Prefab enemy sprites overlapping each other

I have an enemy prefab that can get into a situation where they occupy the same space.

When this happens, the animations overlap, and the sprites start to look a bit odd, as if they're blinking, or just generally not behaving correctly. Outside of occupying the same space, they're fine.

Is this a problem I can handle using sorting layers somehow? Maybe the order in their layer, during instantiation?