/u/AlotOfReading provided an answer to another /r/AskHistorians thread that may be of help to you, "During Manifest Destiny why did the United States not try to annex all of Mexico and the rest of Central and South America?"

Followup question: In the previously posted answer it is argued that racial concerns were a major factor - that a large faction in the US did not want to annex a territory full of non-whites. I understand why a sufficiently racist person wouldn't want to give the vote to the Mexicans, but that seems to assume that there is no option between carving Mexico into full-fledged states, and leaving it reduced in territory but still sovereign. Couldn't Mexico have been made into some sort of vassal state, a "protectorate" or some such formula, with an American garrison in Mexico City to ensure that the newly-installed friendly government did as it was told? Or alternatively, made a colony with a governor-general, as with the Philippines fifty years later?