Ambrose calls you to his office, and says that you have progressed far after what the normal students manage, and that Ravenwood's Professors can't teach you any more. so he sends you to bartleby'[s canopy, and you find: The Ravenwood School for highly advanced students. A much more Magical academy, where each school has it's own distinct Building and there are new professors and magic to learn from. Plus, star, moon, and sun have their own Schools, and in isolation, the Shadow school.
No, I don't think there is a second school of magic in Wizard City. Bartlyby told Merle Ambrose never to use Shadow Magic, so there would not be a Shadow School. Sorry, but I don't think IF we leave Ravenwood we won't go to a different school of magic.
Man i think ill add the profs names just for a suggestion *hint hint KingsIsle*
Female, Salamander wearing a dark purple dress and she leans down on a cane maybe? Name: Noura Oasis
Male, Ice Colossus Looks just like the minion, Name: Stachan FrostWise
Female, Tall and Intimidating Woman wearing a long black dress with white ruffles at the ends and dark green eyes and wears dark green Nail polish. Also, her hair is black with a green tint. Name: Vanellé Crow
Female, Salamander wearing a dark purple dress and she leans down on a cane maybe? Name: Noura Oasis
Male, Ice Colossus Looks just like the minion, Name: Stachan FrostWise 
Female, Tall and Intimidating Woman wearing a long black dress with white ruffles at the ends and dark green eyes and wears dark green Nail polish. Also, her hair is black with a green tint. Name: Vanellé Crow