![enter image description here][1]

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][2]*  
**1918-1939    Czechoslovakia**  
*1939           [Carpatho-Ukraine Republic][3]*  
**1939-1944    Hungary**  
*1944-1945    Czechoslovakia*   
**1945-1989    USSR**  
**1989 -        Ukraine**  

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

  [1]: http://i.stack.imgur.com/NVv2Z.png
  [2]: http://en.wikipedia.org/wiki/West_Ukrainian_People%27s_Republic
  [3]: http://en.wikipedia.org/wiki/Republic_of_Carpatho-Ukraine