Jin doesn't really go out of her way to catch mon so her team isn't especially large to begin with, but that being said, she does bring all of her mon with her basically everywhere she goes.
Alternatively, Mary has a fair number of catches but they are all more of the result of her tendency to visit haunted locations for fun so her collection of ghost friends tends to grow. But much like Jin, she brings almost all of them with her. The ones she doesn't hang back at home with the family while she's traveling.