Mr. D is correct but it seems pretty clear, based on everything I've read, that Honda dropped the Odyssey to avoid dealing with warranty issues from people who didn't follow the proper procedures. From what I've read, the Odyssey and the CR-V, which is approved for 4-down, share the same drive train through 2013.
Here's a link to a thread that addresses all of this. Note that it says that 4-down is ok through 2013.
http://www.irv2.com/forums/f85/2011-...ad-258786.html
Both Roadmaster and Blue Ox sell baseplates for the Odyssey through 2013. Roadmaster explicitly excludes Touring, Touring Elite and transmission cooler models. The Touring models have a different drive train and I can only guess that the transmission cooler issue is one of fit. If you have a transmission cooler it's probably worth checking with Blue Ox to see if their's will fit.
Clearly there's a risk involved so one needs to make their own decision but it's a risk I'm willing to take with my 2011 (not yet equipped for towing).