Leanne,  It sounds like what you have is something known (though
not by the general public) as a "mosque."  Mosques are multi-doored,
tower-like music boxes whose compartments are designed to hold small
objects, such as perfumes, liqueur bottles, cigarettes, jewelry, etc.

I believe Reuge, the one surviving Swiss music box manufacturer,
still makes mosques.  You will see some examples of the type at

  http://www.musicboxshop.com/90243b.html
  http://www.silvergiftstore.com/hanmusmosbyr1.html
  http://www.austriana.com/musicboxes/reuge-mosques_dolls.html

Matthew Caulfield