I think I found what you need. If you go to the animation timeline and change the type to dope sheet, you should see an option next to it that lets you change the type to action editor. This will let you add new actions and save multiple different animations in one rig.
Not entirely sure how you would do it but I think that you may be able to make only ...
Every object that you want to rotate (by script) has to be shild of an Empty Object, so the script responsible for the transformation, has to change the rotation of the Empty Object.
Rotate(Vectors3.up * value) will really be the Y (Unity) axis.