Question play blender animation while simultaneously overriding bone ROTATION ONLY via script

Hi, I am trying to do something very specific. I want to control the rotation of the head bone of my cat character via script. While the cat is running around, the head move relative to the rest of the body in a somewhat realistic manner (im not a professional animator LOL) it bounces slightly while running, turns to the left when turning left, etc. I want the head position to be controlled by this animation, but I want the rotation to be affected by script. I have read some posts suggesting this can be done in LateUpdate(), but im not sure if this will do what I am describing. Again, animation controls position, I just want to override the rotation, ideally additively (ie take the rotation set by the animation and then use script to add x degrees of rotation). Is this possible?

Thanks to you pros out there you are life savers.