F*ck you four elements, I've got one hundred and eighteen...
Nature of Magic:
Stoicheomancers, or Elementalists, believe that everything in the world is composed of matter, and that all matter is composed of small particles of a finite set of "pure", "fundamental" substances (elements). They claim that even such aetherial things as the air we breath is made up of such tiny particles of matter, just spread out further. By understanding the nature of the elements that make up everything, the Stoicheomancer can enact fundamental changes on the nature of reality by changing the elements within a thing or the way those elements are arranged and combined.
Further, they postulate that their are nearly a hundred different "pure substances" in existence, including such things as lead and gold, and that, while they can be combined, not even wishing could turn one pure substance into another -- much to the consternation of practitioners of traditional alchemy. More traditional mages and alchemists point out that these theories are obvious bullox, as every well-educated sage knows that there are only four elements.
Method of Casting:
The key to a Stoicheomancer's spells is the catalyst, a particular element or combination of elements (often an acidic or volatile one) which, when exposed to the base matter of the universe causes it to change in some way. These catalysts are often stored in small glass vials, and must be carefully prepared for each spell, taking into account both the desired effect to be created and the target of that effect -- since an Orc may be made of different elements than a Dwarf, and different sized targets require different amounts of the catalysts. Thus a Stoicheomancer's spells require a great deal of preparation and forethought, but can be cast simply by throwing the correct vial at the correct target.
A Stoicheomancer's spells take the form of complex formulae, resembling mathematical equations but written using symbols that indicate the various elements, which describe the reactions between those elements. They have much in common with alchemical texts, but are much more complex, and are all but indecipherable to those without at least basic alchemical training.
The Limit: (i.e. Why does this guy have Vancian spell-slots?)
Stoicheomancy is no where near as simple as alchemy, and is not just a matter of 'bottling fire', as some laymen think of it. The complex calculations involved in finding the right catalyst and amount of catalyst for the right situation is very taxing on the mind, especially in the heat of battle when one does not have the luxury of writing out the formula on a blackboard. While in theory a Stoicheomancer could keep using his magic indefinitely so long as he had a ready supply of the correct catalysts, in reality, after a few uses, even the most intelligent and experienced Stoicheomancer will become confused and likely to lob a vial of element that is in no way reactive with the chosen target. A Stoicheomancer who has exhausted his daily allotment of spells simply can no longer think fast enough to figure out the right catalysts to use until he has had time to rest and relax his mind.
Breaking the Limit:
A Stoicheomancer who has exhausted his daily allotment of spell slots can attempt to cast additional spells, so long as he has additional catalyst to use, but is likely to select the wrong catalyst. He must make an Intelligence check to cast the spell, with a penalty equal to the spell's level. On a failed check, he has selected a catalyst that is inert with regard to the chosen target and nothing happens (other than the loss of the catalyst). On a natural 20, he has selected a catalyst that reacts, but not in the manner desired. Roll for a Wild Magic surge, with all effects centered on the target of the catalyst.
Just don't call them potions...