In 1865 Brunei offered the US a lease on North Borneo (modern Sabah). The American Ambassador accepted the lease, scared the hell out of the British, and one month later sailed to Hong Kong and sold off the lease to the British. The US government didn't care that much for the whole ordeal. It was bit more focused on reconstruction at home than it was on Imperialist desires.
In OTL the British feared the US would use North Borneo as a coaling station and would eventually expand its power in the region. An American power base in North Borneo was a spear pointed straight into the heart of British-Chinese trade. From North Borneo the US could have easily expanded into British Sarawak and later posed a threat to British Malaya and British Hong Kong. It also would have been an easy way to flank the Spanish in the war that was inevitably going to occur eventually between the US and Spain. North Borneo could have ended up with the US carving out a massive East Indies/Trans Pacific Empire. The Ryukyu Kingdom seemed pretty vulnerable to a sort of Hawaiianization scenario and an established US could have turned Brunei into a protectorate and later a colony. Considering all these places had low populations, the US could have immigrated them into demographic domination. Manifest Destiny wouldn't have ended with with the west coast of America, but with the western edge of the Pacific. Conflicts with Britain in East Asia also could have tanked the future Anglo-American special relationship. North Borneo could have been a pretty big POD.
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Controlling the Falklands would have benefited the US greatly. Considering the Nicaragua canal was an impossibility with Britain controlling the Moskito coast and British Honduras, and being the only major colonial power (Spain was second rate by this time) with the most territories in the Caribbean Basin, Nicaragua was too insecure to be of use. Panama wouldn't be an option until 1903. All US ships going from one coast to the other had to pass the Falklands, so it would have been very good to have. It likely would have made the US more prominent in South American affairs. Considering in TTL the US keeps Liberia, there could be a network of ships going from a US port, in this case Miami, going to Liberia, then the Falklands, then perhaps an annexed Easter Island, followed by possible Clipperton Island purchased from the french, the a final journey to the west coast.
Such an elaborate network of ports kind of reminds you about all the effort the British put into securing lines to India.