The Periodic Table we currently use is already at element number 118 - Ununoctium. Now I'll stop here for a moment to preempt those that would say that many of the newer elements have extremely short half-lives and are of no real significance in this discussion. My argument is that no matter how short their half-lives, they can still be demonstrated here on Earth. The so called synthetic elements and others are still elements or they wouldn't be in the Periodic Table.
Ununoctium was discovered in 2006 and it would be naive for anyone to declare that this is the last element we shall discover here on Earth. There is absolutely no reason why our 118 elements and others still to come should not be discovered elsewhere in the universe in the future.
After all, many of the additions that have been made to the Periodic Table since Mendeleev would not have occurred without advances in technology. Technology does not stand still, and as we progress, more elements will come to light. both on Earth and elsewhere in the universe.
It would be arrogant of Man to think otherwise