I'm not sure what the general idea would be, but lately I've been thinking that the Eastern Militiregnum specialises in Alchemy while the Western does in Magic, with Britay, Ankoria and Morcia each maybe having a different domain of magic. For instance, Morcia has magic of artefacts as N_B also suggested. Britay's magic would be more like elf magic. I have yet to decide what Ankoria's magic's desicive point would be.
I'm coming up with ideas, but I like the idea of different geographical areas studying different arcane arts - though I'd like to think that alchemy is still quite rare/disliked. I'm not trying to insist that what we've created is some kind of special snowflake - don't worry! :P But I'm personally too invested in the prejudicial side of alchemy to back out now.
When it comes to different arts, I was trying to think about the inhabitants of the Fire Desert - i.e., Blaine's home. A few cool ideas thus far, but no solid branch of magic. Oh! And I've been coming up more creative alchemy uses.
As for Ankoria... well, if I remember correctly, that was where the Morghai (spelling?) lived, and they were basically the planets antagonistic force for a while. Perhaps necromancy, mutation inducement, summoning, blood manipulation...? There are plenty of creatively evil ways to use magic. :P