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I think the Carpathian Ruthenia area (the little triangle on the "end" of Czechoslovakia after the end of WW1) gives us five bona fide separate national entities and more if pseudo-states (such as your Fiume) and other periods of loose or brief control are allowed.

up to 1918 Austria-Hungary
1918 Hungary
1918 West Ukraine
1918-1939 Czechoslovakia
1939 Carpatho-Ukraine Republic
1939-1944 Hungary
1944-1945 Czechoslovakia
1945-1991 USSR
1991 - Ukraine

I've marked in bold where nation states were recognisably exercising full sovereignty over the area. Looser claims in italics.

Memelland (now Klaipeda) in Lithuania is another possible candidate.