Is it possible for Latin America to be united under one government? during the early 19th century, I know men like Simon Bolivar certainly thought it was possible. Could it be possible for there to exist three or four states in Latin America (not including Brazil)?
 
Three or four states possibly, a single unitary state would require a modern POD with some sort of Latin American EU. I do not think it possible for a 19th century unified Latin American state to exist post Spanish rule. Among other things the geography of the continent does not lend itself well to it at all.
 
A way would be for the Iberian Union to survive, leading to a unification of Latin America (including Brazil), another way would be for the Spanish monarchy to flee to America during the Napoleonic wars (as the Portuguese monarchy came to Brazil, so Brazil remained united ), Another way would be to bolivar survive and conquer the turkey gradually expanding to the southern cone. Another would be an expansionist Brazil leading the alliance of the Hispanic nations against Brazil, perhaps a Brazilian-US alliance during the Mexican-American war leading to a mexico-colombia-peru-argentina alliance
 
Since so many attempts were tried and failed in OTL the best way would be to look at them and see what PoD you could do to change the outcome. The fact there was so many attempts and none succeeded makes me feel it is almost impossible. Attempts OTL- First Mexican Empire included all of Central America except Panama. Central American Confederation, all of Central America except Panama plus Los Altos of Mexico. Bolivar's proposal which Chile and Argentina refused to attend and Brazil was not invited. Gran Colombia, included Venezuela, Colombia, Panama, and Ecuador (subsequent territory lost to Peru and Brazil); union of Upper and Lower Peru (Peru and Bolivia); Nicaragua, Honduras, and El Salvador attempting to revive the Central American Federation. Even successful Latin American nations have had problems staying together. Mexico has had revolts from Yucatan, Chiapas, Freedonia, Texas, California, Sonora, and the Republic of Rio Grande, and even today with the Mayans.

Geography problems have lead to too much in cultural differences and especially in the 1800s a problem with too far/difficult for timely communication and movement of people and goods and cultural diffusion.

A Trans-American highway at an early age or a larger interest in a merchant marine could help. But Spanish colonial policy never allowed for the colonies to develop such as the 13 BNA colonies did. And the Trans-American Highway in OTL was a USA-led project during WW2 and once that was over it fell away from completion since it was no longer a strategic help to the Super power.
 
What if San Martin and Bolivar decide to work together, which would encourage the Peruvians to work with the Colombians, and San Martin in Argentina might allow that state to be stable enough to also participate.
 
anything is possible, but in this case, highly unlikely. there's too much geographical issue to go along with an overall warlord structure throughout south america.
 
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