This won novella awards from both Hugo and Nebula in 1991.
isfdb.org states: "The book version of this novella was slightly expanded and published soon after the first appearance in IASFM." The novel version did not win any awards.
This review is based on the novella.
A con man approaches a professor who is an expert on Hemingway's works. The con man suggests it should be easy to make passable fakes of some early stories Hemingway lost the manuscripts for (and which were never seen again). The professor is reluctant, but the trust fund which has made a considerable part of his income is about to run out and his wife wants him to do the fakes.
However, there are entities that look after events that would cause unwanted effects in a number of parallel universes. They don't want him to do this and are willing to kill him to prevent him from writing the fake Hemingway stories. But it turns out this professor isn't as easy to eliminate from the multiverse as other people.
His consciousness ends up spending time in several universes. Each time his position seems to become stronger and the entity's weaker. There's really no explanation for this.
Many readers will like the parallel universes and/or Hemingway threads to the story. However, some readers will find it has more of a fantasy feel than SF.
In a note at the end, Haldeman tells us a number of details about Prof. Baird is based on Haldeman. These include the facts that both are professors in the Boston area, they both like trains, they both were wounded as soldiers in the Vietnam War, and they have both studied Hemingway.