If we're talking about theory, it's not just possible but certain that there are more elements than those listed on the periodic table. An element is defined by the number of protons in the nucleus. You can theorize a new element with 69420 protons, and that's that.

What's harder is having that new element actually exist. Elements only get on the periodic table if we can actually observe them existing. Since the middle of the last century, physicists have known how to slam atoms into each other to create heavier elements. Any element heavier than uranium does not occur naturally on Earth and has to be created in a lab. We have created several elements this way.

There is therefore recent precedent for expanding the periodic table. Scientists are actively working on expanding it further, but it is difficult work. These super-heavy elements are very unstable, and creating them requires a lot of time, energy, and expensive equipment. On top of that, the process is fundamentally random, so each try has only a small chance of success.