Totally ASB, but here's a scenario. The British win the American Revolution, but lose to the Franco-Spanish Armada of 1779. Britain becomes a Catholic nation ruled by Bourbons. The Loyalists of the Thirteen Colonies fail to retake Britain and seek a European sponsor. Prussia and Sweden and the Netherlands, as the last Protestant countries, become the new sponsors of the Thirteen Colonies. Prussia with the largest army, recruits most of the garrison force in the country, settles veterans in Louisiana, and eventually becomes hegemon of North America when Sweden declines to Russia and Netherlands declines to France.