Something that requires the raid (especially tanks) to avoid as much damage as possible.

Just having high damage output that can kill anyone hit by it is one thing, but that kind of all-or-nothing is boring and frustrating. A mechanic that limits either mp or healing could work better.

Greatly reduced mp regeneration would mostly affect healers, and forcing healers to be efficient with mp puts pressure on the entire raid to perform. DPS would have to kill faster, and tanks would have to reduce damage taken.

A side benefit is this kind of fight encourages some of the lesser used abilities. A Paladin could heal/stoneskin and use Riot Blade, for instance.

Soft enrage would be healers running out of mp. The fight becomes easier as every member of the raid gets better. Dps do more damage to end the fight earlier, and tanks need less heals.

Obviously this is kind of difficult to balance with all the different abilities all the jobs have.