This may be something incredibly minor but after the American Civil War the United States contemplated buying
Greenland, the Danish West Indies, and even Iceland, however by 1870 that idea failed to get through the Senate.
Now here's the fun part: Saint John and Saint Thomas, two of the three main islands which make up the Danish West Indies/the modern U.S. Virgin Islands, actually held
a binding referendum in 1868 about a prospective sale to the USA and got passed with 98 percent of the vote (though the turnout was unknown). If the Senate had voted in favor of accepting that referendum result, the United States would've paid 7.5 million dollars for them. Saint Croix wouldn't have been included, but Denmark was very open about selling it to the US, too.
In theory this could've even resulted in Denmark keeping St. Croix for a while, maybe even selling it to Germany like Copenhagen considered IOTL after the 1870 sale fell through.