Just one of several ideas I've been considering for the Before 1900s thread. The main point is the establishment of a Japanese settlement in northern Taiwan. I am not sure how workable is this TL, and how many changes can result, but I'll try.

- 1594 – Based on suggestions by Ryukyuan king Shō Nei (long considered to be a ruse to divert Japanese resources away from war in Korea), Toyotomi Hideyoshi attempts to set up a forward base in the Taipei basin in Formosa for a direct attack on China. Imjin War grinds to a stalemate (OTL)
- 1596 – Imjin War ends. Efforts focused increasingly on Formosa instead.
- 1600s – By now, the fledgling outposts set up by the Japanese are under constant attack from tropical diseases and aborigines.
- 1609 – Battle of Sekigahara, Tokugawa victory. Small numbers of Pro-Toyotomi supporters flee to Formosa, creating the Nanryukyu Domain. Satsuma forces conquer the Ryukyuan kingdom and pursued the Toyotomi loyalists to Nanryukyu. However, despite subjugating the domain, heavy losses pressed the Satsuma to withdraw with relatively generous peace terms, retain the daimyo as a vassal to Satsuma, and by extension, the Tokugawa, but otherwise independent.