Instead of three groups of two classes each (tangible, intangible and supernatural solutions,) why not two groups of three each linked to the standard abilities? Three natural/mundane classes -- Fighter (Strength,) Trickster (Dexterity,) Charmer (Charisma) -- and three supernatural classes, including the modified Cleric (Wisdom) and Magic-User (Intelligence.) That leaves a supernatural class with Constitution as a prime ability, relying on innate spell-like powers; a good model for witches or psionicists or a replacement for a 3e-ish sorcerer.
Call them the Gifted:
- they solve problems with supernatural gifts;
- can feel supernatural forces around them;
- have one innate power per hit die.
The Gifted cannot change powers or learn new ones; they are born with one power, with new powers manifesting every time they gain a hit die. They cannot have powers with a level higher than their hit dice, nor can they have more powers of a higher level than those of a lower level. As a shortcut, use any of the existing spell lists as lists of available powers, with slightly different features based on the power source: Clerical powers require choosing an alignment, Druidic powers require regular communing with nature, MU powers can be dispelled, and Illusionist powers can be disbelieved. Powers from different sources are not normally mixable.
I'm open to other suggestions for a better class name. If I were to rename Clerics to Spirit-Workers (to resemble "Magic-Users",) perhaps this class would be the "Power-Gifted""? Not completely satisfied with that...