Read everything carefully, including the warning disclaimer at the end.
To stack two TC-E's, you need to modify your TC-14E slightly. Grab a lens and your TC-14E for comparison. On the rear of the lens you'll see three long "tabs" on the inner part of the mounting ring. Now look at the front of the TC-14E. You'll see two long tabs, but where the third long tab is on the lens you'll instead see a medium-length tab and a short one (sort of looks like a long tab with a notch taken out). You need to remove the smallest tab. To do so, you should first remove the mounting ring from the teleconverter.
You'll see four small screws that hold the ring to the teleconverter body. Be careful not to strip those screws when removing them, as they're usually quite tight. Also be careful when pulling up on the ring—there's a thin metal ring inside that can be damaged if you use force. (If you're at all worried about doing the modification yourself, most camera repair shops can make this modification for you quite quickly, and without damaging your teleconverter.)
With the ring removed, file the smallest tab completely off. Be sure to remove every last bit of metal debris caused by the filing. Re-attach the ring.
Now, mount the TC-14E on your camera body, then mount the TC-20E on the TC-14E, and finally mount your lens on the TC-20E. If you're using a lens with an f/2.8 aperture, you might even find that autofocus still functions reasonably well on a D500, D600/D610, D750, D800/800E/810/850, D7100, D7200, D7500, D4/D4s, or D5.
Warning: Obviously, this modification voids all Nikon warranties. If you aren't skilled with tools and don't understand the instructions 100%, don't attempt this at home, folks! Take your converter to a reputable repair shop, explain what you want done, and let a pro do the job if you have any doubts at all. Also note this: with that tab removed you can mount the TC-14E on lenses that aren't supposed to allow teleconverters because their back elements may hit the TC's front element! In these days of litigation for litigation's sake please also read and understand this: Thom Hogan is not responsible for any damage to your converters or lenses, because you're going to attempt this modification only if you agree that you are the one responsible for anything that goes wrong. If you don't agree to absolve me from all possible damages, then please go back and un-read my answer, making sure to forget any details or where you might have seen them.
