The Final Fantasy Legend (Makai Toushi Sa·Ga in Japan) is one of my favorite Game Boy games. You can find excellent Let's Plays of the game here and here, and some of it sequels have also been given the Let's Play treatment at The Let's Play Archive.
One of the playable races/classes is the mutant, and the most interesting feature of mutants is their ability progression: They randomly have up to four magical powers at all times, and those powers are randomly replaced with other powers over time. The player cannot control which abilities are replaced and what they are replaced with. You could wind up ditching a useless power for an awesome one, or vice versa. Mutants can still use weapons and other items, so they generally aren't rendered useless by a bad set of powers, but the random aspect of their abilities adds an interesting tactical dimension to combat and resource management. "Here's what my mutant can do right now. Let's take advantage of that while we still can."
Here's an idea I had for adapting the mutant as a class in Lamentations of the Flame Princess:
Mutants are people who have been touched by fey or eldritch forces and forever altered by the experience. In fact, they are constantly altered by the energies with which they have become infected. Their fates and identities are at the mercy of one or more unknown beings or stimuli which shape them like putty, changing them each day. Their appearances may shift subtly over time, but the mental and magical changes they experience are quicker, more dramatic, and more profound.
Mutations of Identity:
Every day upon waking from rest (not upon waking from a Sleep spell), or every 33 hours if rest is not taken, whichever comes first, roll 1d10 on the following table four times to learn the Mutant's current abilities. Multiple rolls of the same result stack.
1. Gain +1 to all Saving Throws for the day.
2. Gain 2 skill points for the day, which are allocated like a Specialist.
3. Gain +1 Base Attack Bonus for the day.
4. Choose one of these four abilities:
1. Fighter Combat Options (Press, Defend, and better Parry)
2. Dwarven Encumbrance (5 extra items before gaining the first point of Encumbrance)
3. +1 to AC when not surprised (like a Halfling)
4. Only surprised on 1 of 6 (like an Elf)
5. Gain one Magic-User spell. Roll 1d6 for the spell level then roll randomly for the spell from Rules & Magic, or choose one spell of any level from the spell book of a Magic-User who consents to let you see their spell book. "Borrowing" a spell from a spell book in this way does not require the use of Read Magic and takes one turn, but the Mutant cannot do this unless the Magic-User gives clear consent. This is a magically-enforced, temporary pact, without which the Mutant cannot "borrow" the spell. The Magic-User lending permission for the "borrowing" cannot memorize the borrowed spell at the same time the Mutant has it memorized; the Magic-User must wait until the Mutant rests or 33 hours have elapsed.
6. Gain one Cleric spell. Roll 1d6 for the spell level, then roll randomly for the spell from Rules & Magic. Casting a Cleric spell does damage to the Mutant equal to the level of the spell. The Forces of Law and Chaos do not mix well.
7. Gain the ability to Exasperate like an Alice from A Red & Pleasant Land one time. (If this is rolled multiple times, the Mutant must wait at least 1 hour between uses of Exasperation, like an Alice.)
8. Roll on the 1d100 Mutation table from Carcosa. Sorry, you're a REAL mutant today.
9. Gain one random Psionic Power from Carcosa. The number of times this power can be used per day is determined by the Mutant's level, as per Carcosa. (Ignore the ability score requirements for Psionic Powers.)
10. One time today, if the Mutant fails a Saving Throw, the Mutant can choose one living creature within their line of sight or in physical contact with the Mutant, and this creature suffers the effect of the failed save instead. If necessary, the universe will do strange and crazy things to accommodate this.
If the Mutant rests, or if 33 hours pass, the Mutant loses all abilities from this table and must roll for new ones.
Other Class Features:
-Experience requirements, HP, and Saving Throws are the same as the Elf. When able to cast spells, their Spells per Day follows the progression of the Magic-User for Magic-User spells and the Cleric for Cleric spells.
-If able to cast spells, the Mutant can cast them one-handed and up to heavily encumbered.
-Mutants have the same magical weaknesses as Elves (such as taking damage from holy water), as well as the same resistances or immunities to certain spells (like Sleep).
-Mutants cannot craft magic items like Magic-Users or Clerics.
-Mutants must be Chaotic in alignment.
-Note on random Magic-User and Cleric spells: If the Mutant rolls a spell for the day that is too high for the Mutant to cast at their level of experience, roll again until a usable result is rolled.