With the amount of low damage from story mode, it sometimes feels very lackluster. I honestly rather they had another category for simplistic mechanics that aren't too complicated to understand, but with higher damage than story content in terms of frequency of attacks + higher damage auto attacks, and make that the "middle ground" mode.
Recovery in the "middle ground" mode would still be more doable since there are less difficulties in resolving mechanics. Something akin to deep dungeons higher floor bosses but with more mechanics and tuned for 4 / 8 players. Criterion bosses is a bit too far into Extreme with the mechanical burden it places on players, and having something that's slightly below that would be a good middle ground for players who don't exactly like the high mechanic gameplay, but still want something tougher than the average boss that tickles like a wet noodle outside of its mechanics.

Then Extreme and Savage fights would be the higher mechanical difficulty fights instead.