Romney, West Virginia bounced back and forth between the Union and the Confederacy a bunch of times; Ripley’s Believe It Or Not claimed it switched hands 53 times, although Wikipedia says it’s closer to 10. Still, that’s only two countries (although France and England had claims to the region prior to 1800).
The Spratly Islands are claimed, wholly or in part, by six countries at present: Brunei, People’s Republic of China, Malaysia, the Philippines, Taiwan and Vietnam.
Eliminating the 1800 rule, Tashkent has been part of the Kangju Confederacy, Sogdians, Turkics, China, Persia, Kara-Khanid, Russia, Mongol Khanate, Kokhand, Soviet Union and Uzbekistan in its recorded history.