I am looking to find out if the Model S has a factory approved "Tow Mode" for 4-wheel towing behind an RV.
Must be on a flatbed trailer. Towing with 2 or 4 wheels on the groud will definitely damage the drivetrain or steering box.
No. Can't tow two wheels down either. But there are plenty of lightweight trailers out there cheap ($4-$6k). Assuming this is to be towed behind a motor home, seems self-defeating. I don't own a motor home but have an F150 pickup and often must tow an 18-foot box car carrier. Doing so drops mpg from around 16 to between 7 and 9 mpg depending on load weight (9 empty, 7 with a 1952 MG TD onboard). It would be worse with a heavy Model S. So you would spend more on fuel to tow the car than to have someone drive it separately. I would not presume to tell anyone how to spend their money, but a Model S behind a gas or diesel guzzling tow vehicle feels like an oxymoron to me...
Use volkerize.com to search the forum for a thread on exactly that same issue from earlier this year. The conclusion was that it would only be possible with lots and lots of modifications to the car itself. Not recommended at all.
Perhaps you can put a "dolly" under each model S wheel.