Stories in the same universe, but not necessarily part of a series. Same Universe, Different Series (SUDS). Maybe.The first thing that leapt to mind was fan fiction. I love writing fan fiction as a way to get myself writing. Without having to worry about creating characters or settings, I can just get into the story straight away. Once I'm there I'll find myself making up new characters for people to interact with and then, sometimes, they even take on more of a life of their own and I start writing stories about them, with only passing reference to the canon characters of the universe they inhabit.
One example of this is Dawn Bell. She started off as a minor character in a Heroes fanfic I was writing, based on a dream I had. Se was just as someone that Peter and Claire happened to bump into and then go off to another adventure. But I really liked her as a character. She'd got an interesting ability, to be able to 'push' abilities from one person into another. In the story she first appeared in I had her push Claire's healing ability into Peter so that he could heal a gunshot wound.
Then I started thinking, what if someone wanted to use her ability to get more power for themselves? And suddenly she was the star of her own story, with just a quick reference to Peter and Claire at the very start of the story and a whole raft of new original characters to interact with.
Same Universe, Different Series.
It's not just fanfic writers that use this trick though. How many stories have been set in the Marvel universe, with crossovers between various characters, other characters making a debut in one series only to go on and get their own stories, and hidden references to other superheroes in various comic books, TV series and films.
I could probably think of more examples, but I'm going to stop there. I'm getting all nostalgic about Dawn Bell now - high time I resurrected her for another adventure, I think...