Looking closely at the Canon Fall 2010 EOS System brochure, page 37 -- the TC 1.4x II and III, and TC 2.0x II and III are shown. Included is line drawing cross section showing the positions of the lens elements.
While is interesting is that both the 1.4X III and 2.0 III have been completely redesigned(which means a chance that those of us with the "now older" Super telephoto lenses may see improvement in image quality), a closer look at the new 2.0x III shows that it can no longer accept a 1.4X (neither II nor III) between the 2.0x and camera body as the final element next to the camera body in the new 2.0X III is no longer recessed.
I don't think adding a 2x and a 1.4x together would worry most people, because most people are afraid of focusing at F/11... I can see why Artie did it, with an 800mm to get that sort of reach
I think he got his maths wrong though... an f/5.6 aperture plus 2x and 1.4x would make it f/16... :p
personally I would rather use a crop sensor camera with the 800 and a 2x to get f/11 and get a similar focal length... although the 1D MkIV may focus better than a 7D when using live view AF