Polytherians identify with more than one species of nonhuman animal.
This is the current terminology. Polytherian replaced the old term Polywere which had first been use in 1996.  It is not known exactly when the term polytherian became standard use within the community. It most likely came into use in 2005/2006 when the term Therianthrope was replacing Were.
Poly is a prefix meaning "many".
Individuals with a great number of non-human identities may be confusing spirit guides as theriotypes.