You can do that in GURPS, its under the rules of Influencing Success B347. Players have the power to use CP to buy success (buying success rule) and influence the kind of success (player guidance). Lastly, you can BRIBE your players to act on their disadvantages a certain way.
If I were to Teach New Players into GURPS, those of a different point of view, I would like to show them this Narrative Side using Wildcards and Influencing Success rules. Actually it is possible to have multiple ways of enjoying the game, as long as everyone gives each other the space or spotlight. You can play GURPS like a simulations or like a storyteller/thespian.
To gamers where certain details matter - , like the number of shots, the halfswording technique, if the armor edge protection, etc... This may not be for you but do try it out.
Influencing Rolls (B347)
I allow buying success rules to spend CP for success
I allow player guides rules to allow the Players to influence the nature of a success.
BUT, I reserve the option to "give" (Bribe) the player CP (1cp only) in exchange for the player to act on their disadvantage in a particular way.
So basically Imagine GURPS Lite with the Core System, Wildcard Skills, and Influencing Rolls and GM bribery. Its like a Fate mishmash with GURPS but the detail can be scaled (or called upon) if you want it to be. Its a great medium for a GM to try out Fate from GURPS, or Fate to GURPS.
In Other Game Systems
Its as simple as making XP into a Currency of Character Development for Bribes and Costs for Dramatic Success. It can be done with any system since you can influence the die roll. the GM can even "recycle" the spent XP or Character Dev Commodity into a "fate pool" when a Player spends a lot of his "points" to alter success they get a different set of incentives and challenges.
Example in a DnD Game, XP is in a currency of Points related to the Level. The higher the level the Higher the Points are worth in XP so it always stays the same to the PC, X no. of points is equal a level. Now the GM Bribes the Players with more XP influencing their character, while the Players spend Xp to influence their Success.
You dont have to stop there, XP spent in this way may go somewhere. This is where some Home brew guys will get a lot of fun. Making XP benchmarks and what it does. It can be based on "Alignment" or the "Class", goes into their reputation, or a secret random kind of fate (a mixed blessing). After enough XP in this "fate pool" something happens. The PC can have kinds of nemisis, a lover that brings problems, a family with a lot of responsibilities, etc... they can have a low level but their Fate has more in store for them than they can potentially handle.