Interchangeable Cloth Objects

I want to be able to have a modular character with various interchangeable parts, one of them being a cape. I tried authoring the cape as a separate mesh, but it’s not colliding with my character’s physics asset. Do they all need to be authored on the same mesh in order to work? I thought making the cape collide with the environment will allow it to sense other capsule parts on the character, but that didn’t seem to have any effect.