No, they don't. Consider what an element is. An atom consists of protons, neutrons, and electrons, and what determines which element this atom is of is the number of protons. That's its atomic number. As you can't have half a proton (if you could cut one up, it would become something that isn't a proton at all), and we know what all the elements are starting from 1, we can be sure there are no more to be discovered, even on other planets.
Everything up to 92 occurs naturally on Earth, and higher numbers have been created artificially but they're radioactive, unstable, and eventually fall to bits so we don't find them in nature. Some fall apart slowly, some fall apart in milliseconds, but they all fall apart eventually.
The only possibility is if there's some totally different KIND of matter that isn't made of the elements in the periodic table, but there's no evidence whatsoever than any such stuff exists. So as far as anybody knows, the periodic table lists everything.