Allow me to clear up any confusion the title may make by mentioning a nice little play called Rosencratz and Guildenstern Are Dead. This is what I would give as an example of a meta-story I refer to in the title (using "meta-story" to make up for not coming up with a better term). Mainly focusing on what would be a kind of ensemble otherwise, the minor characters that usually relate to a plot very little.
Is it possible? To make a story out of a bunch of irrelevance when attention should be elsewhere? Maybe tread the line of Seinfeld, a role play about nothing. Honestly the idea has only been swimming around in my mind, I have no guarantee it could work. But fun is still part of the question... Yea? Nay?