Pronouns

Q. Hello CMOS. My close friends and I have decided for numerous reasons that all of the current methods of political correctness in pronouns are silly and, simply put, not as gender neutral as they claim to be. With that in mind we decided to import the French on as both a singular and plural gender neutral pronoun. However, it has just recently occurred to me that in this situation what would be the protocol for the genitive case of on and constructions such as his/herself, would it be on self? Thank you CMOS.

A. Well, when on decide to create on’s own grammar, I would say on get to make up all the rules onselves, n’est-ce pas? Bonne chance!

[This answer relies on the 17th edition of CMOS (2017) unless otherwise noted.]