The trinity is like this class pyramid. just replace fighter/rogue/mage with dps/tank/healer and its effectively the same thing.

Use it on any rpg system and the characters/classes will fit somewhere into the pyramid. You'll almost never find any archetype with a complete lack of ability to perform the other 2 archetype's functions.

The issue is that there's no other way to interact with health bars than the trinity based on your specific definitions of each archetype

DPS - You focus on dealing damage. Ranged, melee, burst, dot, magical, physical, it doesn't matter.
TANK - You focus on taking damage. Dodge tanks, enmity or not, defensive skills or defensive stats.

SUPPORT - You heal damage, and you facilitate in the dealing or taking of damage by your party members. That facilitation could be buffs/debuffs, or more indirect advantages/disadvantages like information

No matter how creative you wanna get with a class, when you boil it down that class is going to be tanking, dpsing, or supporting.