Mike:
Years ago, Coore and Crenshaw built a third nine holes within the grounds at Southern Hills in Oklahoma. But, I've never heard anyone even mention it since it opened.
Most of the 27-hole courses I've seen are mediocre, or a mess. It's hard to build a third nine that is equal quality with the rest, if the original 18 is very good. Visitors and members and certainly raters just want to play the "best" 18 holes, whatever they are, so attempts to mix up the nines for the course of the day usually fail.
As Kalen and D_Malley suggested, what most clubs really need today is a place for beginners and kids to go out and get better and enjoy themselves without getting in the way of the members who want to play 18 holes. Shinnecock built a crude par-3 course in front of the clubhouse a few years ago for that very purpose, and it seems to be reasonably well received at a low operating cost.