One thought is you could build (mostly by recording cases as they happen) a scale of numbers for various narative twists the players ask for/would benefit from. Then you can either have the players pool and throw as many dice as they like to try and reach that number (good for a lower scale) or have them just spend dice and have every die count as its max value plus modifers that player has for action dice (higher scale). Either way, using a target number allows "lucky" character builds to utilze their full oomph beyond the simple pile of dice.
So you could have "minor NPC flips to players' side" as, lets say, a "20". The players could all throw dice in, rolling with their bonuses and if the total reaches or exceeds 20, bamm, turns out Joe Guard has always had a grudge agains the evil overlord and this looks like the time to settle the score. If the players just add full value (less variability, less chance of going, "aw crap, we spent 5 dice and got nuthin'...") I might set that to more like 35. Blow six 6-sides and you know the worm will turn.
Only other rule that comes to mind is each kind of narative event can only be invoked once per adventure. Minions R Us does have some standards... Angry, infiltrating Joe Guards are screened out for the most part
. The point is for the players to increase the fun (at a reasonable cost) not to let them get in a rut.