Identities are not roles. One may say “I’m a business man” or “I’m a father.” But if you ask him about his identity and he say first “I am a Catholic,” that is something fundamental about him, and he cannot have many things in his life of that importance.
You cannot have too many identities either. You need to put these identities into a hierarchy. The most important one is on the top. It is the culture construction of meaning by a social actor.