Best chance of the US to hold Canada

In what moment, from the Independence to WW2, do you guys think the US had the best chance of annexing Canada as several states and holding them in the long run?

I know there's a lot of timelines with this happening, but I wanted a more "accurate" analisys of this possibility.

I'm ok with realeasing Quebec if you think so.
 
Does a pre-ARW that still leads to an English-speaking republic with 3 branches of government lead by person with veto power that occupies modern USA and Canada count?

Or take one of those lame TLs where the CSA wins the Civil War and the USA annexes Canada... somehow. I really don't get why getting beaten by 3rd rate slave nation makes the North suited to take on the strongest power of the world.
 
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