Sorry, missed the "private" part. Scratch off all of the public/resort ones I listed.
Brian,
They may have separate memberships, but it's still Pinehurst CC. They themselves boast of 8 courses, not 6. Members at 1-6 can still play 7 and 8 for a fee.
Chris Kane,
I agree. Same goes with The Country Club in Brookline, which is rated as a composite course, or at least it used to.