Can parts have different animations?

Development Character & Animation
,
1
  1. There are separate parts for the left and right arms.
  2. The left and right arms have different skeletons from the base character skeleton. One may have a reverse joint or an additional joint.
  3. Both have the same animation set (idle, run, jump).

In this case, is it possible for each arm (left and right) to be attached directly to the base character, instead of using retargeting, allowing them to perform the same animation set?