So you want for example: Add an animation (change position) of a gameobject and while doing that: Add another animation(change rotation) the game object. (for example a car tire). right?
Or do you want to animate a child of a game object, while animating a game object? (for example: moving the forearm and moving the upper arm )?
In both examples you should just do the animation in 1 animation.
Mixing animations is not clean and also should not be necessary.
Just set the Keyframes with all of your game objects together .
As long as you have parented them corrects, it should behave as planned.
I agree with alexo1001. Unitiys standart mecanim "animation-maker" is pretty weak.
I stumbled about tons of limitations while using it. I suggest you download other animation addon for unity.