Early on in US history the Yucatan tried to join the country and was only narrowly rejected over concerns that it would be a slave state.
After the Mexican-American war Polk wanted the US to expand all the way to modern Santiago de Queretaro and could have easily done it but the guy who ultimately negotiated the treaty on the US' behalf was against the idea of US expansion so negotiated against the US' own interests.
If those two decisions had gone the other way then it seems likely that all of Mexico if not all of Central America would be part of the United States today.
After the Mexican-American war Polk wanted the US to expand all the way to modern Santiago de Queretaro and could have easily done it but the guy who ultimately negotiated the treaty on the US' behalf was against the idea of US expansion so negotiated against the US' own interests.
If those two decisions had gone the other way then it seems likely that all of Mexico if not all of Central America would be part of the United States today.