For ideas on classes we can look to other Final Fantasy games (because SE is much more likely to make a new class out existing FF lore than create something unprecidented/new).

The Final Fantasy Tactics series (FFT, FFTA, FFTA2, FFTAS) has tons more classes not in FFXIV.

Here are some caster ideas:

Seer
Oracle
Illusionist
Green Mage
Mathmatician