Last year I attended a singing workshop. We sang quite a few rounds simply divided into three or four groups. After a while the coaches got us to walk around the room quite randomly. At the time it sounded good but just seemed like a bit of fun. I see now that it combined JeffB's round suggestion with Rapunzel's choir master's mixing.

If the singer needs to learn the harmony, one of the computer tools such as Melody Assistant or Finale Notepad might help. Midi tunes can be created for all vocal parts and either played independantly or combined.