Despite its name the Equestria Trainers' Society does not strictly adhere to ponies, although certain races may find they are more welcomed than others. Below is a description of how each race is received in the society.

Unicorns, Pegasi, Earth Pony - All regular members / slaves

Zebra - Welcomed into the society as more exotic Members or Slaves.

Gryphons - Although not used as slaves (it's for the training of Equines, after all), they are allowed to join as Masters and Mistresses.

Dragons - In the past, Dragons were not permitted within the society because the safe house was too small to accommodate them. However, with some help from a certain purple dragon whelp, branching chapter houses were created, and now Dragons are acceptable Masters and Mistresses.

Minotaur - The society uses Minotaur as guards and handlers to take care of the Slaves when their Masters and Mistresses are otherwise preoccupied. However they are not officially part of the society, and thus do not take part in its more exclusive privileges.

Diamond Dog - Absolutely NO! These slobbering, simple minded beasts are not the kind of rabble the Equestria Trainers' Society would be caught dead associating with. Unless they were being mugged in the streets by said rabble!

Other Races: May be added later according to how they are presented.

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I like this layout for the races. It is actually pretty close to what I had in mind for them to begin with. I especially like that you put that gryphons can be owners, but not slaves. Good work.