One narrative mechanic I love in A Penny For My Thoughts is a bit where you pause at significant moments and ask two different players what might happen next. One player suggests a thing, then the other player suggest a different thing. Then the player we're focusing on chooses one of those two events to be the true one.
It's very simple, but it creates interesting narrative easily. It adds nicely to the game's dreamlike atmosphere (so might not be appropriate to all games/stories) as you have vague memories later of things that never happened. It also means that at least two players approve of and like the proposed story path (the one saying it and the one choosing it). Sometimes the options created are very different, sometimes they're nearly identical except for one small detail. But the questioner always has a choice to make.
One thing I've been doing with a lot of games that I make is combining that mechanic with a random, ambiguous input. Things like Tarot cards or pulling random words out of a hat/off a list. You draw a Tarot card or whatever, then you ask two different players to interpret it, asking how it applies to the story you're currently telling. And each offers a different story path forward. (I find that Tarot cards aren't perfectly suited for this purpose, but a similar deck specifically built for the job can be really effective.)