We have been having discussions about stacking 1.4xTC III and 2xTC III on telephotos. I have done some testing using a 70D, and here are some brief conclusions, incorporating what others have already written and discovered.
1. Stacking requires a 12mm extension tube placed between the two TC III extenders.
2. The 2xTC III must be attached to the lens and the 1.4xTC to the camera.
3. The camera exif records only the effect of the 2xTC - the pair attached to a wide open f/2.8 records as f/5.6.
4. The 300/2.8 focusses manually at all the usual distances, and the same is reported for other telephotos.
What I found from the 70D today is:
5. AF works only at intermediate distances (approx 30-80m, give or take) and not closer or at infinity in both live view and phase detect. (The 5DIII also didn't AF).
6. IQ is quite good.
Here are two shots of Egyptian geese at about 20-30m. The stacked TCs required manual focus which I did through the viewfinder, rather quickly, resting the lens on the ledge of a hide. The full shots are reduced to 1200x800, the crops of the heads are 100%. The goose standing is done with just the 2xTC attached. The sitting goose with the 1.4x + 2x.
Both are wide open (f/5.6 with 2x, f/8 with 1.4x+2x), iso 640 and 1/3200 or 1/1000s.