Basically, everything the USA acquired before 1898 became a state, it was how we operated. There may be some small island that I am forgetting, but the USA model was to acquire (buy, conquer) and administer as a territory. Non-white minorities were not allowed power (Native Americans, Slaves, etc). US would encourage settlement by the giving away of free land (often moving off natives first) and infrastructure such as railroads. Once their are enough whites to pay for a government (25K to 100K), it would petition Congress and become a state.
That only works for territories that either have small enough populations to outnumber or are contiguous and thus the native populations can easily be moved.
Hell, the only reason Alaska and Hawai'i are'nt still territories is because the government realized they could/would be used by the Soviets as legitimate propoganda.
If Borneo was admitted, it would likely follow the same pattern. Direct rule by the US Federal government, displacement of natives, and moving in white settlers.
North Borneo had a population of some 285,000 in 1936. In 1865, the population would have been much smaller and could have been immigrated into submission when referring to a white majority. There'd probably be a considerable amount of Chinese, Japanese, and other sorts of Asian peoples moving in, but only as a minority, even if a significantly sized one.
With a more "cooperative" white population in north Borneo, I could see the US controlling the Philippines more easily. It may even "Americanize" certain regions (significant ports) to the point where it can keep them while "liberating" the Philippines later.
Borneo was on the other side of the Ocean and more importantly was simply not somewhere that could be settled i large numbers due to its position in the Tropics and the diseases that come with it.
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