jml, the above posters correctly summarize that you can do open jaw OR stopover.

I did JFK-CDG-JFK-LAX this spring. I had stopovers in CDG and JFK (about 24 hours). Then went on to LAX where my award ticket ended. I stayed in LAX for a few days and then made my way home on one way tickets with a discount carrier and AA (there was another stopover in between). For me, I was able to make good use of the 160K Concorde award, which included that extra leg to LAX in B/E. Be creative.