I've written a few short stories now set in the same universe - one which I have been building for a while with an eye to perhaps setting a book there in a future project. They are very much separate stories, though they might share characters, and occasionally events of one story may impact another - but each one stands alone as a separate, self-contained narrative. What I want to know is, is this a good idea for trying to get these works published? If I have a short story rejected by one publication, is there likely to be any negative connotation of submitting another which may share a setting and characters? I have heard of several authors doing exactly this (Susanna Clarke, for example), but is this an unusual thing to happen, or do publishers not mind writers "recycling" settings like this?
There would probably be no Larry Niven as we know him today were it not for this very dynamic. His Known Space books and stories answer to the very description you give and are perennial favorites of mine.