After you have achieved the game’s first ending and proceeded to Chapter 6, you can increase the level cap of your jobs from 12 to 15 allowing you to unlock all sorts of new and powerful abilities. To do this, you must complete a variety of trials located in the Halls of Tribulation. There are 7 gates to the trials and each one unlocks a different set of job’s levels.
Halls of Tribulation I (Halcyonia Region)
Halls of Tribulation II (Halcyonia Region)
Halls of Tribulation III (Savalon Region)
Halls of Tribulation IV (Wiswald Region)
Halls of Tribulation V (Rimedhal Region)