Here's a link to the places that Ritz Carlton has timeshare availabities:
With portfolio membership, you'll own a collection of unique luxury vacation properties with renowned service and quality worldwide.
www.ritzcarltonclub.com
If you look at the resort directory, you'll see that none of them trade there. They do trade in
ThirdHome, though. The exchange fees there are a bit higher than in Interval, though. Depending on what timeshare you own, you might be able to establish an account with them and try for one of those. If you're interested, let me know and I can give you some hints on getting started with them.