The other carriers I fly (UA, NW, CO, US) permit open jaws but do not allow stopovers.
Actually, at least CO BusinessFirst award flights can have both an open jaw and a stopover- I just booked one that has both. I would assume the rules apply also to coach award flights, at least to Europe. The only restriction on the stopover that I was quoted was that the stopover has to be along the most direct route. Ie, going Paris -> Seattle, they aren't going to fly you CDG-HNL, 2 day stopover, HNL-SEA on the way home. But a stopover in NYC is fine.