That's actually similar to what a friend of mine and I are trying to create for our own RPG. A spell casting system where the magic user actually creates their own spells, by combining certain factors and effects.
For example, you'd have one effect, like ice manipulation. You can add a targeted effect, like Self, Single target, or AOE.
So a self targeted defensive Ice spell would be Ice Armor. A Self targeted Attack Ice spell might be an ice Punch, or adding cold damage to your melee attacks. You get the picture.
It could even work for Illusions. Self, target, or AOE, is the difference between Disguise Self, Silent Image or Major Image. Audio and Visual can be other aspects you could add to the spell.
As a Character grows in power, they get access to new abilities, and new forms of 'metamagic' since that's what it really is, but no ability can be used without at least one Metamagic, and you have to choose from the beginning how to use that.
Like, at level 1, you decide to pick Fire as a "spell effect". It states that a foe hit by a fire attack gets 1d8 worth of damage per level up to 10d8. But you can't access the "Target" effect until level 3, or the AOE effect until level 5, or something like that. So you can really only do touch attacks with it until you learn better shapes. Maybe by level 9 or something, you get the "Wall" shape.
But there is no "Fireball" spell. It's just the "Fire" spell, shaped as an AOE. And of course, whatever "Shaping" effects you add would increase the 'spell points' it requires, or whatever system you have in place.
Everything else, such as appearance of the spell or whatnot, is just fluff and up to the character. Like the skeletal hand of Chill Touch. Why a hand? Why not a tendril of smoke? That should just be fluff, and up to the player as to how it looks.
But you'd basically be mixing and matching effects with shapes and various other abilities, literally creating your own spells.