Can the Animate Dead spell be cast on a zombie?

One of the players in my game is a Death Domain cleric and enjoys having a small army of zombies accompany him. We had come to a situation where it is not plausible for him to keep the zombies with him for the 24-hour period, but he spent the change (on a government writ) to get them locked up until his return, so he can try to regain control over his minions.

Is it possible to cast Animate Dead on a Zombie and have the spell work as normal? Is a zombie considered a corpse, technically?

Also, if you say that it should work in theory, here comes the sticky part. He also wants to use this spell on a Mummy Lord (that he doesn’t know is a Mummy Lord, yet). Does it simply not work, since it’s an undead creature and not a corpse?