How would I make my character support layered clothing

I cannot figure out how to make my mesh support layered clothing.

Character:


When I attempt to add layered clothing to the character, this happens:

I have looked for tutorials, and looked at some of the documentation. I have tried copying the wrap target from the normal player to that character, changing the cage mesh to the character’s mesh. The character is a humanoid, rather than an animation controller. Any help would be appreciated.