White Carbuncle that focuses on DoT damage/support abilities for ACN, (since it's in the class artwork, but we don't have one in game).....

Defensive oriented Fairy who's skills add barriers or damage reduction for SCH.....

Honestly, the only reason I can see that Summon III is a SMN only skill is because they were lazy and didn't want to have to create a third pet for ACN and SCH.....