I was researching the Thunderbird legend for a drabble and I found that a lot of tribes actually believe their people are decendent from these creatures who are able to take on human form. It got me wonder about how the idea of Animagi could fit into this, but something has me stuck.

Can Animagi only transform into ordinary creatures or could they possibly become magical creatures too? We see that with the Patronus charm, it can be both, but what about this?