I will leave it to you to determine where this fits on the timeline of one lifetime, but the Florida Parishes of Louisiana were a Royal French Colony until 1762, when they were briefly ceded to Bourbon Spain before being taken over by England in 1763. Spain took them back and ruled until they transferred the territories to Napoleonic France in 1800, who promptly sold the rest of Louisiana to the United States in 1803. In 1810 the Florida Parishes revolted against Spain and formed an independent nation, the Republic of West Florida, which is also the original Lone Star state (the flag was one big star on a blue field). They merged into the US and became part of the state of Louisiana. In 1861 Louisiana seceded and briefly formed an independent nation before joining the Confederacy. So between 1762 and 1862 a small area in Louisiana was governed by 8 different sovereign nations, at least if you count Royalist and Napoleonic France twice (and consider the independent nation of Louisiana and the Confederacy sovereign states).
I am not sure if it is the most, but if someone was born in the are of Galicia during WWI one could have an interesting life. Born in Austrian/Hungarian empire one could then be Ukrainian, Polish, Soviet union, German, and then either Polish/Soviet union again.
Here is a map from 1914 so you can see where it is, and how it will be in trouble/invaded a lot of times in the 20th century.
Transcarpathia (now in western ukraine) is a good example, just like the already mentioned Galicia.
I'll copy here my comment from an earlier thread:
I'll include not only the different "owners" but the names of those owners, which could appear on newly issued documents.
I. Part of Hungary -1919
I/1.: The Austro-Hungarian Empire, up to 31. October 1918
I/2.: The independent Hungarian Kingdom, 31. October 1918 - 16 November 1918
I/3.: The Hungarian People's Republic 16 November 1918 to 21 March 1919. (On the 21 December 1918, the territory becomes the Ruska Kraina autonomy)
I/4.: 21 March 1919 - april 1919 still an autonomous territory, now part of the Hungarian Soviet Republic
I/5.: Czechoslovakian/Rumanian occupation april 1919 - 10 september 1919 (during which for a short time the Hungarian Soviet Republic recaptured part of it)
During 1918-1919 the short lived West Ukrainian People's Republic laid claim on the area, but never occupied it.
II. Part of Czechoslovakia 1919-1939
II/1. Part of Czechoslovakia, without autonomy 10 september 1919 - 9 october 1938
II/2. Part of Czechoslovakia, with autonomy 9 october 1938 - 2 November 1938
II/2. The southern territory becomes part of Hungary, the rest is part of Czechoslovakia with autonomy. 2 November 1938 - 14 march 1939
III. Independent Transcarpathia 14 march 1939 - 16 march 1939
IV. Hungarian Kingdom 1939-1945
IV/1. Part of the Hungarian Kingdom: 16 march 1939 - 23 november 1944
IV/2. Part of the Hungarian Kingdom, but under Soviet occupation 23 November 1944 - 29 june 1945
V. Soviet Union 1945-1991
V/1. As a independent member of the Soviet Union 29 june 1945 - 22 june 1946
V/2. Part of the Ukrainian SSR 29 june 1946 - 1 december 1991
VI. Independent Ukraine 1991-
Since the independence of Ukraine (1 december 1991) Transcarpatia is still a county of Ukraine. There was a vote for an autonomous status in in the early 90's, where the autonomy got an overwhelming support, but it never materialised.
TL;DR: Transcarpatia was part of 5 different countries and people there could have held 9 different passports during the 20th century.
The concept of country doesn't apply strictly to the territories of the of the Holy Roman Empire, but the Herrschaft (fiefdom) Jever changed owners very often as the inheritance was disputed and enforced by different authorities. The fiefdom was ruled by:
Living in Moselle during the late 19th/20th century, you'd be French, then German (1871) then French (1918) then German (1940) then French (1944).
I'm sorry, but this is asking for a rather speculative "through out history" answer, as I'm unsure there is a clear one.
However, it is a pretty interesting thing to wonder, and I would suggest contacting /u/caffarelli, who runs Tuesday Trivia, and seeing if you can work this into a theme for that.