So, your challenge is to make United States as large as possible, but stays stable and unified as superpower today...
I've been thinking about Phillipines, Taiwan, Liberia...as well as Greenland and Caribbean Islands maybe...?
About Canada and Mexico...there is a theory that if US tried to annex them (let's say Canada in 1812 and Mexico in 1848), the resulting "United States of North America" might has been collapsed and disintegrated in 1880s into smaller nations/states (Quebec, New England, Virginia, Lousiana, California, Texas, etc)...simply because the Union government didn't have the menpower and the resources to put down three simultaneous rebellions...
But I'd like to know your opinions about this topic...