The US is not going to invade or conquer Mexico without a legitimate casus belli. After the Mexican War, the United States has not only settled all existing territorial disputes, it has practically gotten almost all possible land it could ever desire from Mexico, absent the Gadsen Purchase and perhaps Baja California. After the Civil War, there is practically no desire for any additional land from Mexico.
The only way I can see this being done is if all central government authority collapses in Mexico and Mexico is controlled by various regional warlords. This is possibly as a result of a prolonged Mexican-French war that sees important uniting figures like Juarez die during the fighting. Once the French leaves, the anti-French forces split in a civil war similar to the 1910s except without any kind of true national government. As a result, Mexican national (as opposed to loca regional) identity collapses and each warlord only sees the importance of expanding their own personal domain.
Confronted with anarchy to the south, Washington decides to send in troops to secure peace and protect American citizens and property along the border and in Mexico. Various liberal factions see the US as the only means to for a victory of liberal ideas and cooperate with the US. Rather than see themselves removed as a force, Mexican conservatives also see it in their best interest to cooperate with the United States as business interests work with US robber barons, and even Mexican Catholics reach out to the large US Catholic population for support and help. Eventually, US occupation spreads to all former lands of Mexico.
After a decade of the "American intervention in Mexico", the northern part of Mexico (generally underpopulated, in a desert, and bordering the US) is eventually incorporated into US territories and will eventually become states. The middle Mexican states (down to say Veracruz to Jalisco) are much more populated and harder to incorproate into the US. However, their culture is still European oriented. They are administered by US officials, but the population is torn between wanting to join the US, to affirm their own separate identity, or to join in some kind of effort to reestablish a united Mexican state. The southern portion is dominated by indingenous people who have no desire to join the United States, but are probably also run by US officials.
The American occupation is likely very controversial. While the northern tier's accession to the US is accepted, it is conceded that the southern tier will be given complete independence as several independent states after a period of US trusteeship (perhaps to end sometime in the 1920s) although some kind of transportation corridor in the isthmus of Tehuantepec is probably secured. Likely the middle tier eventually reconsolidates into some form of united Mexico under US sponsorship, and often dominated by US business interests. For the first 30 years, revolts and such are low as people are simply thankful there is stability and peace. However, afterwards there is greater agitation for self rule which may turn to violence depending on how the US reacts to it.
At some point, perhaps ranging anywhere from 1900-1940, the "American Raj" ends and all US troops and administrators return to the US (now with a border south of the Rio Grande). The several decades of US rule in Mexico remains extremely controversial especially as a renewed Mexican nationalism in "Mexico" (now confined to central Mexica more or less the old Aztec lands) views the US intervention as dividing a united Mexico. Mexico continues to have problems with the other independent states of Yucatan, Chiapas, and Oaxaca/Zapotec as the question of whether "Mexican identity" requires the entire area to be united, or if "Mexican identity" is limited only to the old lands of the Aztecs. Although long standing ties from the US occupation period remains, by the 1960s a confident series of states in the Old Mexico begin to overturn any remaining unequal treaties and address the US area of influence in the Isthmus of Tehuantepec.