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With a POD no earlier than July 4, 1776, can anyone find a plausible way for the United States to have a small posession in Europe by the beginning of the 20th century? If not, then by 1935?

I don't want a Yank wank, just a small posession, no bigger than a medium sized state. My goal is to force the USA to pay more attention to Europe overall, especially in the days leading up to the Great War, or failing that, World War II.
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