Zilliogender

 is a term for having an indeterminately large number of genders.

Definitions

 * Zilliogender: having zillion genders. - arco-pluris, July 31, 2018

A zillion is not an actual number, and used as a huge but nonspecific number. Zillion sounds like an actual number because of its similarity to billion, million, and trillion, and it is modeled on these real numerical values. However, like its cousin jillion, zillion is an informal way to talk about a number that's enormous but indefinite.