An X-Dice Mechanic for D&D

This is a rough sketch of an idea, not a full implementation. Just putting it down here.

Hit Dice. Every character in D&D, no matter which Edition, has Hit Dice. They're an integral part of the game.

At least since AD&D (and maybe Greyhawk?), different classes have had different size Hit Dice, but originally all classes had D6 HD, and gained them at different rates. Only Fighters got one every level.

What if we built on this original conception, but expand to new kinds of Dice? The first two categories that immediately jump out at me are Skill Dice and Magic Dice.

Classes are now differentiated in two ways - 

1. Classes gain Dice at different rates. Fighters have the most HD, Thieves the most SD, etc.

2. Classes can use their Dice for special abilities. Anyone can "Find Traps", but only Thieves can use their Skill Dice to "Remove Traps". Only Clerics can use Magic Dice to "Turn Undead" and Paladins use them to "Lay on Hands". 

Hit Dice become a more widely applicable mechanic than just rolling Hit Points. Instead they're a general stand-in for your combat ability, and might be used to disarm someone of their weapon, push them over a cliff, or otherwise perform a combat "stunt".

Multiclassing is easy and painless. You simply have the greatest number of dice available to you from any class (not the sum). A Fighter 5/MU 5 would have 5 HD and 5 MD.

Spells effects (such as Fireball damage) are determined by the number of Magic Dice you have, not your level.

More ideas to come as I flesh out the concept.