Workflow for adding animated cloak to character

Hello guys. I am having some problem in understanding what workflow should I follow for adding an animated cloak to a character.

I have used Adobe Fuse for generating a model. Through Maxima, I exported the rigged model into Unity. I also used the Third Person Controller Animator included in the Standard Assets (originally on the model Ethan), so in practice is a full working character that I could potentially use.

However, I need to change the character.
I need to add a cloak to the character. This is a type of cloth that is not supported in Fuse so I need to do it myself. I am willing to do that in Blender. However I would also like the cloak to be animated properly when the character moves. How do I do that?
I already have the animation included in the ThirdPersonController. I can change the animation in Blender. However, as far as I can see, those animations specify the movement of the rig, not the movement of anything else. But in this case, I need to move the cloak, which is not part of the rig!
Even if I added a cloak in the Character generated by Fuse, how do I apply an animated cloak to all the animations?

Of course I could make the cloak a “fixed” part of the model, so that it does not actually animate independently. However I would like the cloak to fly around when the character jump, or just to move a bit when he is standing still. But this would require different cloak animation for different character animations. How do I do that?


EDIT: Just to clarify. I don’t just want to add a cloak. I would do this with the cloth simulator in Unity. I want to add a full body cloak, let’s say something like this alt text
I wasn’t able to get satisfying results with the cloth simulator.

Best way to do this to get the most satisfying and predictable results is to rig the cloak model then create custom animations for each state (jumping with cloak, landing with cloak etc…). There’s lots of tutorials on rigging around the internet.

You’ll never get desired results using Unity cloth.