Xenogenders
"Xenogender is a nonbinary gender identity 'that cannot be contained by human understandings of gender; more concerned with crafting other methods of gender categorization and hierarchy such as those relating to animals, plants, or other creatures/things.' Xenogender isn't defined in relation to 'female' or 'male' (the binary genders), but by other kinds of ideas that most people don't think of as having to do with gender. When people talk about nonbinary gender, they often find that there aren't any words for their experiences." - Xenogender Wiki
I also recommend reading this thread for more information from a personal perspective.