What is the easiest way to switch out animation clips at runtime?

What I want to do is have the character play an animation given by the equipped item. Is there any way to switch out animation clips on a per character basis? If you use a animation override controller, that affects every single animator that uses the same controller. Can I create a new instance of an animation override controller per character or is there some other way to do this?

Creating an animation controller that has every animation clip in it is possible, but that would get unwieldy with a large number of items. I'm looking for a more extensible solution.