While I totally don't know why one would want this, it's certainly possible. From a standard Ubuntu (with Unity) installation:

1. Install kubuntu-desktop




2. In a terminal within the Unity desktop, try to run the KDE desktop like this:

   
   
   

   nohup plasma-desktop &
   
   

   
   
   

   ^{The nohup somecommand & pattern makes it run in the background and independent of the terminal you're running this in. (specifically, the process spawned isn't a child of terminal in the process tree, but given to the mother of all processes - init.)}




3. optional If you like this and you want to make it permanent you can create a startup script:

   
   
   
   
   

   • Create a text file (with for example Gedit) startkde.sh, containing

     
     
     

     #!/bin/bash
     
     # sleep seems necessary - getting kdeinit I/O errors otherwise
     
     sleep 3 && /usr/bin/nohup /usr/bin/plasma-desktop &
     
     

   
   

   • Make the file executable, from Nautilus (file properties), or by running chmod +x startkde.sh

   
   

   • Open Startup Applications from the Dash.

   
   

   • Add an entry "KDE" and browse to the script.