Tonight I had the urge to stack the TCs on my Sigma 500/4.5. The last example got me to about 1960mm, stacking the Sigma 2x + Sigma 1.4x + Tamron 1.4x, which is effectively the same FOV as a 3136mm if you consider the 20D's 1.6x crop. With the 2x + 1.4x, the moon just about filled the frame top to bottom. With all three converters, the moon didn't fit in frame.
Here is the Sigma 500/4.5 + Sigma 2x TC + Sigma 1.4x TC (1400mm), scaled for web:
And here is a 100% crop from that image, with zero post processing:
And here is a 100% crop from the Sigma 500/4.5 + Sigma 2x TC + Sigma 1.4x TC + Tamron 1.4x TC (1960mm):