What if a different type of atomic nucleus existed, aside from particles governed by the strong force, that electrons could form orbitals around? The orbital patterns would probably be different as well, producing a whole new type of atom right alongside of those in the periodic table. We can use this concept as rubber science to explain made up chemical elements often named in sci-fi series, especially in Star Trek.
We can even speculate further that atoms can comprise of both strong force particles and said hypothetical particles, warping electron orbitals even further. We can then chart out a two-dimensional table of chemical elements with linear progression for the intervals of each set. So in this case, let's then assume there are 118 hypothetical elements by themselves (if ever proven possible, it probably won't be exact). That's 118 hypothetical elements plus 118 strong force nuclei elements plus 1182 possible combinations, totaling 14160 possible chemical elements. You can forget naming them at this point.