Ars Magica has a set of 5 techniques (to create, to perceive, to change, to destroy, and to control) and 10 forms (animal, air, water, body, plant, fire, image, mind, earth, and power). You can combine the techniques and the forms to quite literally create effects of that combination on the fly, and then research spells for easier/more powerful spells of a more fixed nature.
Depending on your abilities in the forms and techniques, you focus on different ones according to your preference, and effectively has a constrained set of guidelines that allows players to (maybe with more than non-trivial effort) cast practically anything they can think of.
The addition of hidden-to-player spells is actually quite simple.
- Don't allow them to read the spellcasting sections of the book.
- Create a physical set of cards. Testing will be needed to see how many copies of cards are necessary. You will need, at least, a card for Range, Duration, Target, the 5 Techniques, and the 10 Forms
- All spells in the game are spontaneous, and follow spont casting rules (which you may want to adjust for desired power level, or allow the research of formulaic spells per the Faerie-Raised magic rules in HoH:MC)
- To cast a spell, players deal out a combo of any number cards in front of them, according to the rules that they have hypothesized. Face down cards should indicate "more" or +1 magnitude. You may or may not want to have order matter.
- They then roll to cast the spell, and you adjudicate what happens.
Examples, assuming order doesn't matter.
Ball of Abyssal Flame CrIg35
Base 25, +2 voice
This produces a pleasantly intuitive effect.
Whereas a slightly more complex formulation would be:
Fire-Fire-Fire-More-More-Duration-More (Roughly translated as Choose the third guideline at the fifth magnitude Which would create light as bright as direct sunlight on a clear day for Sun duration.
Thus, most of the games would start out being "WTH do all these options do?" as there is plenty to explore, and this formulation will give you an easy way to rule on what amounts to thousands of recipes. Encourage players to document their experiments, as they will be frequently deadly. Use as much of the Ars setting as fits.