What system works for a campaign where powers show up randomly during play?

If you want the power reveal to be part of the game, the system matters less than the structure around it. A lot of superhero games assume you build the sheet first and then start playing, so random powers can get messy unless the rules already support surprise abilities, discovery scenes, or temporary unknown traits.

One useful route is to use a point-based system with broad powers and let the actual effects be rolled or assigned behind the curtain. That way the player knows their character is changing, but not exactly how. It works especially well if you give each power a clear theme, then let the table uncover the exact expression over time instead of rolling completely blind every time.

The cleaner option is a system that already has mutation, escalation, or transformation built in, then use randomness only for the details. That fits the tone you described better than a fully open superhero engine. You get the fun of discovering strange abilities, and the game is already expecting characters to change as they go.

If you try to make a standard superhero toolkit do this with pure randomness, the results can be swingy. One person gets a cool utility power, another gets something awkward, and the whole thing can start feeling unfair unless the group is okay with that chaos. If that chaos is the point, great. If not, you’ll want a more controlled reveal process.

If the main goal is for players to not know their powers in advance, you can do that with almost any system by having the referee generate the powers secretly and only reveal the results when they come up. The important part is giving each power enough mechanical definition that it can be discovered fairly at the table, not just described vaguely after the fact.

I’d avoid going fully random on every detail. Random theme, random trigger, maybe random scope, but keep the core rules consistent. Otherwise you end up with a lot of rerolling and edge cases, which can kill the mystery pretty fast.

My pick would be something lighter and more flexible rather than a crunchy superhero simulation. Crunchy systems often assume you know exactly what your powers do, while a looser engine can absorb weird random abilities without turning every interaction into rules archaeology.

You can make the randomness part of the setting too. Maybe the powers are unstable, maybe they change under stress, maybe the characters are all basically test cases for something bigger. That sort of setup does a lot of work for the tone and makes the random generation feel like story material instead of a gimmick.