I tested my 5D MK III with 2 TC's, and it worked with a 70-200mm f/2.8 but slowly. Other lenses ranged from not at all to unreliable AF. I also found AF to be inaccurate. The in focus light flashed and the shutter opened, but images had varying degrees of AF accuracy.
I decided it could not be trusted except on the 70-200mm f/2.8, and with 2 TC's stacked on it, IQ was far from what I'd want with a huge investment.
Also note that when you stack TC's, only the one closest to the camera reports, with Canon TC's, it reports the wrong aperture and focal lenght.