Can I separate parts of animation (2D)?

I have an object with a sprite. At runtime this sprite gets a random color at start.
I made a lot of animations to this object, and these animations gets the color it was assigned at start.
Now I made an animation (on Piskel) separated into 2 layers. One consisting of the object, and another layer with some effects on top. I conveniently made it so they play well together.

Here's my question, can I separate my animation into layers likewise in Unity?
So that my effects stays with the original color, and only the layer with the object gets the randomly assigned color? As far as I can understand, Unity "Animation Layers" isn't exactly the same as the ones Piskel call "layers"

 

Animation Layers are generally used for controlling different body parts of a model with different animations. I'm not even sure how useful they would be for sprite animations.

I know nothing about Piskel, but a better equivalent to their layers might be simply having multiple objects in Unity so you can animate them individually and stack them in front of each other like Photoshop layers.