Aniexe / Anief / Aniem / Anieu
These are terms for nonhuman headmates in a system who, due to being nonhuman, do not identify with the human idea gender. Instead, they may subscribe to a sort of proximal-gender, where they are a certain gender but without the human ideas and concepts.
An example is a dog who is male, but since they are not human, they do not identify with the human concept of male. Instead, they are male-proximal. This headmate would be aniem.
Aniexe: An nonhuman headmate whose closest human gender is agender / gendernull. Pronounced annie-ex.
Anief: An nonhuman headmate whose closest human gender is female. Pronounced annie-eef.
Aniem: An nonhuman headmate whose closest human gender is male. Pronounced annie-em.
Anieu: An nonhuman headmate whose closest human gender is nonbinary / androgyne / genderqueer. Pronounced annie-oo.
These terms are open for every system of every origin.