Greetings,
This does not surprise me. I know there are sites that tell you how to do it, but Canon says don't do it.
What I might recommend is buying a longer lens.
It is possible to stack Canon teleconverters, by fitting a 12mm extension tube between them. The extension tube is needed because all the Canon teleconverters have a protruding front element that will physically interfere with stacking them with another teleconverter... and in fact limits the lenses they can used upon. The space created by the extension tube prevents the front element of the one teleconverter from interfering with the rear element of the other. Whether the lens will be able to focus to infinity or not with this extension really depends upon the lens.
Both the images below were shot using Canon EF 500mm f/4 IS USM lens (1st version) with EF 1.4X II and 2X II extenders stacked behind it. Focus was done manually.
This first image was a test to see how if the lens and extenders would work. The black tail mule deer was probably about 1/4 mile away. The image isn't great... probably due to camera shake. Even on a sturdy tripod and with IS working, 1400mm is a lot of focal length to try to keep steady. PLUS, this was on an APS-C camera, so the effective focal length was more like 2240mm!
Above image was not cropped and took a lot of work in Photoshop to make it at all presentable. Even then, I wouldn't ever display it very large... Probably no more than, say, a 5x7" print. It just doesn't have sufficient quality for anything larger.
This image is a composite. The moon was shot using the same 500mm lens with 2X and 1.4X on APS-C digital (both of these images were done with EOS 10D... all of 6MP!). The wolf was photographed a couple years earlier using a film camera (Elan 7, if I recall correctly), an EF 28-135mm lens and 550EX flash. She was a beautiful "ambassador" wolf who visited schools in southern Oregon or could be visited at the sanctuary where she lived.
Dakota had been found injured beside a rural road. She'd been shot. She was nursed back to health, walked with a bit of a limp, but always was a really sweet girl... not a mean bone in her body. Unfortunately she died about a year after this photo was taken at around 6 or 7 years of age. The bullet from years before had just done too much damage.
I always liked this photo of Dakota, but wasn't happy with the plain black background. So one clear night I decided to try some moon shots. This time I had better luck keeping everything steady on the tripod. In fact I ended up softening the details in the moon a bit, while compositing the two images in Photoshop.
Once again, both the deer and the moon had to be focused manually. The AF systems of the cameras couldn't handle the effective f/11 aperture of the f/4 lens + 2X + 1.4X. (I don't recall which extender I put next to the camera and which next to the lens... or if would make any difference.) However, the EF 200mm f/2 is two stops faster AND the R6 Mark II is able to autofocus at least two or three stops lower light conditions than any of the DSLRs.
So, it is possible. But it may mean manual focusing and may have a lot to do with the specific lens used with the stacked teleconverters. In this case, the 500mm has enough leeway "beyond" infinity that it's no problem using the 12mm extension tube between the teleconverters. That may not be the case with a 200mm lens.
EDIT: FWIW, both the shots below of small birds (Anna's hummingbird and bush **bleep**) on their nests required an extension tube on the 500mm lens to make it capable of focusing a little bit closer. I'm pretty sure I used a 36mm tube in both cases (a Kenko, Canon's longest is 25mm) in order to make much difference in the lens' minimum focus distance. If I recall correctly, that particular lens' MFD is about 15 or 16 feet. No teleconverters for these images... just a fairly large amount of extension to be able to focus a little bit closer.
Now THAT'S HILARIOUS! I got "bleeped" over the name of a bird! Hah! 😎
Spoiler alert, the name of the bird is only three letters, starts and ends with "T" and has an "I" in between. Didn't even occur to me that it might get bleeped! 😁
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Alan Myers
San Jose, Calif., USA
"Walk softly and carry a big lens."
GEAR: 5DII, 7DII (x2), 7D(x2), EOS M5, some other cameras, various lenses & accessories
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