Yes of course!
According to current Democratic party beliefs there are at least 7 genders (or was it 72?)
Including: male, female, transgender, gender neutral, non-binary, agender, pangender, genderqueer, queergender, queerqueergender, non-queerqueergender, third gender, fourth gender (ect) two-spirit, three-spirit (ect), and all none or a combonation of all of these. To list just a few. And then this muliplies if people want to wear animal costumes. And probably more for the French.
Confusing?
No worries.
There are undergraduate and graduate degrees in gender studies on offer.