Same Animator, Different Animations

Lately I am discovering that I would love to have a feature which uses the same animation "structure" but allows me to change the animation clips (and maybe transition times).
I have a lot of different characters which all have more or less the same behaviors (give or take a few unique abilities) with different clips for each one, such as "idle", "attacking", "walking" and "dying".
If feels stupid that I have to duplicated the same animator for each character just to place different clips there and if I want to make a change to the behavior (such as having the attack be activated by a bool rather than a trigger) I have to make the change for each unit one by one.

Does anyone have a unique solution to the situation? Is there something which already does this that I am missing?
Do any of you have the same issues?
What are your thoughts on this?

 

Animator Override Controllers are exactly what you're looking for. They're implemented kind of badly, but they get the job done.