It’s what if the US tried to get and wanted an empire. Do to the facts that they were a colony many people wanted to US be without any but in this timeline compromises are made to give the colonies levels of representation and that they’d (mostly) stay within the America’s. With an argument of being them better structure and stability like the Romans.
A bigger amount of emphasis is made to the military earlier on and with the war of 1812 they annex most or all of Canada. Maybe allowing Ontario and Quebec to stay as Canada where they only take most of the west or if they take more than Ontario and Newfoundland would also be taken, including what ever island the Americans can get during the chaos of Napoleon taking Belize. Than it’s manifest destiny away, eventually the Mexican-American war happens and the US wins this time taking more of Mexico’s north and the Mayan territory where the Americans kick‘s out all the Mexicans and send them to Mexico. this eventually starts another war but instead of annexing it or turning it into a colony they turn it into a puppet since they can’t control such a dense and rebellious state without a constant large military presence.
In this timeline agriculture is more important and with the south having more power laws that could damage agriculture has a harder time to pass so probably no civil war. William walker would’ve also convinced the US to annex Nicaragua, so they turn it into a colony, and with the civil war not happening I can see Lee and Grant being sent by the American government to help defend Nicaragua during the Williams wars and conquer the rest of Central America. Eventually I’m the 80’s(1884-ish) the US would ban slavery which would help its other colony thanks to the new migrants. The US occupation of Venezuela would turn it into a colony and then the Spanish American war would give the US cuba and Puerto rock to colonize enough to turn into states in the future while the rest of the territories in Asia would stay in the same course.
With this more colonial US the republicans would allow Roosevelt to run again and get us into world war 1 earlier and if we go with the English than maybe in exchange for territory that Britain has in South America, I can see that as something that the US settles on.
Although that’s the original timeline especially since Theodore likes Britain but if Germany was the Ally (unlikely) than the central power would win with Liberia expand to the border of Germany’s colony and Liberia would expand closer to the center of the continent. The rest of the european holdings in the America’s will be given to the US, Quebec would be a separate country but would either have all of its English territory take or it would unite and allowed to keep the english up north to be connected and allow the US to have more influence because of the majority English population. if the massive Us uses there navy to put pressure on Britain and start an invasion of oceania they would take New Zealand and maybe Australia if the Australians help rebel(though Theodore did like the British so he might give them a good post war deal either way).
Although I see the US just sticking with Britain so after consolidating their new territory they would go back to influencing and annexing parts of south america leaving military bases in the Philippines.
Than japan, well I’m mean... they‘d lose pretty quickly but the Japanese probably wouldn’t be turned into a colony because of the issues with the Philippines. although the Japanese can keep Taiwan while Korea gets independence so they can keep a better eye at nationalist China