Perhaps the Boxer Rebellion as a POD? Where the Western powers are even more intent on protecting their missionaries and, when the Manchu emperor refuses various European demands to post soldiers throughout the country to defend the Christian westerners, the US and the other Western powers decide to use their own troops to do it themselves?
The Europeans are based out of their respective ports, but the US lacking (as far as I know) a port, takes Taipei, and ends up basically imposing itself on the whole island. When China falls to revolution (even earlier than OTL surely due to the emperor's kowtowing to Western demands), the Western powers incorporate their supply ports and the territory immediately around them as Overseas Territories.
I'm not sure when/if the United States would actually incorporate Taiwan as a state, but I do imagine that once the mainland falls apart, it'd fall under commonwealth status not unlike Puerto Rico. Thus, like Puerto Rico, cue a massive debate in the US pretty much identical to that island, however, add in even more resistance on account of the sheer distance, since there's no plans (either OTL, far as I know or TTL) to create a 'bridge' of sovereign territory across half the Pacific due to the unincorporated nature of most Pacific islands. That said, a POD like this could very well push for the incorporation of the Pacific island territories into recognized, incorporated, territories.