Ah, thanks for this, it's exactly the kind of response I was hoping for.
It's definitely been done before, I can think of a few things along similar lines in various genres. In my fuzzy view of it, it'd work like the cross-story reader was a camera, moving through the world, settling on one scene, seeing it out, following a thread, branching off, settling on another scene etc.
e.g.
Story 1 - Halfway through the protagonist crashes his car, deals with the policeman, moves on with the story
Story 2 - The protagonist as a policeman, dealing with a car crash before getting called away in his story, catches his thief on a tip from a newspaper seller
Story 3 - The newspaper seller story about going home and murdering a loan shark etc etc
...and it works with just the witnesses of shared events too, not just character-relay. Like that movie I can never remember the name of, because the title is just the time. Next to impossible to google too.
And behind all the stories there's an election going on, or an earthquake and the resulting clean up or whatever.
I mean, not that, obviously, that's rubbish, but that kind of loose framing structure.
What I like about this idea, is that I'd be pretty much compelled to figure out each story from the get go, in a coherent pass, to make sure they fit together as whole as well as individually. And that means I'd have to answer a lot more questions about the world than would be necessary for one story on its own, but the resulting detail might enrich each story individually. Plus I'd only have to understand one world for many stories.
It's never going to work is it? Sounds like fun though.