I think there used to be a few but they are long since gone.
I've only ever really used Tengu, and this is some of the stuff I remember so the same commands might apply to other character:
Spinning lariat - half circle forward, punch
Charge throw - back, towards, punch
German suplex - towards + punch (when close, grapple move)
Big slam - down, up, punch (when close, grapple move)
Even bigger slam - towards + punch while enemy is groggy (randomly happens when you hit them a few times, once again this is a close grapple move)
The winning tactic for pretty much the entire game with Tengu is ground the enemy with the charge throw, then when they wake up you do a meaty jab into the normal big slam. On bosses you usually just use the spinning lariat.
Ara Ararauna, Blue and Gold Macaw, 32-34 inches
They are adaptable, and enjoy being in social situations. They readily become adept at performing tricks, and seem to love doing so. Cost:$900-1400