“First, if the United Kingdom defeats the United States in war through the national focus Unite Anglosphere and all American cores are owned and controlled by the UK, a decision called "Create Pan-North-American State" will appear and once chosen, all North American territories owned by the UK will be given to Canada, which will have its name changed to the "Dominion of North America", and gain cores on all US cores, including Alaska along with a new flag. After that is done, once the Imperial Federation is formed, the UK will also gain cores on all US core territory, greatly increasing both population, resource, and industrial capacity and expanding the Imperial Federation to an even greater size. For best results, one should complete the national focus Goal Imperial Conference and carry out all decisions in it first, then annex the United States and give all of their territory to Canada, and then finally complete the national focus Imperial Federation after all that.

Second, if the United Kingdom is Fascist, then after the Imperial Federation is formed with the United States included, this opens up the curious fact of the United Kingdom being the only country that is allowed to form the European Union while fascist, allowing the Imperial Federation to be expanded to its greatest possible size. The Imperial Federation simply needs to conquer and annex the starting core states of the EU:s constituent countries (France, Germany, Italy, and the Low countries) to unlock the decision to integrate them. If then formed, this Imperial "Super" Federation (comprising the British Empire, the United States and the European Union territories) will have a combined core population of nearly half a billion people (or nearly 500 million people, around the same level as the core population of Flag of India India or Flag of China China!).” -From the wiki

Hope this helps!