Increase regional integration in the Americas, something which is pushed for early on and led by the United States (it won't work without it). Things come together so that the subordinate governments of Latin America, cowed by American imperialism and economic might, eventually vote to become states of the new American Union, which is dominated by the United States. Does that count?
If not, then build the conditions for a communist revolution in the United States and when the Great Depression hits, America becomes a communist state and begins to openly support communist movements throughout Latin America. The American communist movement gains a pan-American touch to it, as do other communist movements (including the Peruvians), and it becomes necessary to free the Western Hemisphere from capitalist imperialism by making one state. The new United Socialist States of America will annex Peru eventually in its conquest of the Western Hemisphere. The USSA is still dominated by US-Americans, much as Russia OTL dominated the Soviet Union.