How to animate the same object in the same time using built-in Animator? (for different properties, of course)

Tech ring image: https://openclipart.org/image/2400px/svg_to_png/183383/tech-rings.png
Unity version: 5.6.2f1

I’ve animated the ring parts to rotate around the center at a different rate. This is my idle state on the first layer.
On the second layer I’ve animated the ring parts to elevate from it’s location. To test this I’ve temporarily chose this as the first state after entry.

Only the first layer worked. I tried additive settings, synchronizing layers, but none of those worked. The synch worked on the state, but didn’t actually play the animation clip, which is really weird.
The elevation animation should activate on trigger later, and I don’t want the idle rotation to stop or change.

How can I pull this off?

Did you try recording the animation? It makes things easier.