OTL USA + CAN + realistically anything else it wants who is going to stop them?
At the very least you're going to see everything that makes up the USA and Canada plus Alaska to complete things. The same forces and impulses that saw a westwards expansion are still going to be there under the British. Mexico is also a possibility if Britain takes it from Spain in a war before it achieves independence.If American of British Empire independence never happened, and the original 13 Colonies remained in the Empire, what could be the plausible size (and borders) of British North America in early-mid XX century?
Possibly. Two factors that potentially mitigate against taking too large a part of the Caribbean are that internally those individuals who already own interests in sugar cultivation will lobby against it so as to avoid competition and internationally they're considered so valuable that they might be better off used as bargaining chips for territory elsewhere e.g. Guadeloupe.Most of the Caribbean as well...
If the British get too grabby though, or give the impression of such, the rest of the world will line up against them out of self-preservation. How interested were the British in areas like the Argentine? I can only think of two invasion attempts that were ever made, one of which was done without orders under the initiative of the local commander, and neither were massive affairs.A British Southern Cone.