Historical fiction abounds with just that sort of thing, and is most interesting because of it!
Hell, even fantasy does it with history. Check out Tim Powers' "The Anubis Gates" for some true virtuoso playing with history.
The trick of course is to make your version of history both compellingly readable, and accurate on all points that can be easily verified. If you can do both, and make your version of history more interesting than any alternative version, then, well, you win!