Removing a debuff that turns an otherwise pitiful attack into the ultimate would simply be a cleansable (possibly typal) vulnerability debuff, e.g. when demanding an Esuna or a tank-swap depending on timing and target. That mechanic we've seen before as well.
We've also already seen some run to an unlit square (T1) or run from patterned AoEs (T9) kinds of arena mechanics, though I wouldn't be opposed to seeing more if they could help create an impressive raid aesthetic.
As for different types of DPS checks, thus far all you have are hard and soft enrages overall (most), hard and soft enrages starting from a certain phase (T6), nukes based on remaining HP of adds or boss phase (A3S), hard and soft enrages based on adds (A4, A6S, etc.), adds that simply add raid damage taken and may or may not be ignored for a time (T4, A2), adds that synergize with the boss and may or may not be ignored for a time, and jails (Titan Ex, A3S). While that might sound exhaustive, that actually still leaves a fair bit, both mechanically and in impression.
Some DPS check mechanics not yet seen:
- Damaging something in order to generate a resource, defense, or healing. (Though both Levi and Ramuh have resources that damage against multiple adds help to retain for defense.)
- Adds that can have conditional or situational benefits to the raid for a time.
- Behavioral manipulation of mobs or bosses based on rate of damage dealt (rather than just %HP reduced total, creating %HP phases, which have still only been especially worth holding out for in T5, T6, and T7).
As for arena mechanics:
- Environmental factors both negative and positive, or either depending on the raid's current situation, to be utilized through positioning of both the raid and enemies, including the boss.
- Greater use of cover (the only real examples to come to mind right now are T7 and A6), perhaps in an environment where pillars and such normally line-of-sight breaking objects can be placed via player and enemy positioning.
- Manipulable enemy attacks (the ability to overcharge a core boss attack to throw off it's aim).
Just a few examples for each.