With a napoleonic POD i can see: In exchange for British support for their revolution Haitian leaders agree to become a protectorate, then during the congress of Vienna they are given the French Windward Isles. A few decades later in a deal with Denmark they buy the virgin isles, from there they control everything but the Spanish possessions and its much harder to get those since they're the almost the entire Spanish empire by that point and this they're much more hostile to losing them whereas the French Caribbean was other than Haiti rather unimportant.