I have thought for years that we should invade and make the Mexican states territories, build a relatively corruption free government and let the people decide in 10 years or so if they want to go back to being Mexico.
America had an opportunity to take all of Mexico, but declined to do so. I can't remember the years, but it was after the Civil War.
During the Revolutionary War, the Continental Congress sent a contingent to Canada precisely to ask for their support in fighting England. And if they agreed the American colonies offered to make them the 14th colony and they would be given complete freedom of religion. The Canadians thought about it and said no.
It might not take an actual invasion. Suppose the next president said to the President of Mexico, “You remember what happened in the 1840s? We’re quite capable of doing it again.” I think he might want to avoid that. Maybe enough to cooperate.