Haven’t seen this answer yet, so I’ll add it here. There comes a point in adding electrons where they’ll have to move faster than the speed of light for everything to work, and according to our current understanding of physics, that is impossible. So while it may be possible to find an island of stability we can create past the current limits of the periodic table, we more than likely wouldn’t be able to go past the point where the electrons would break laws of physics.
I wish I remembered the atomic number that phenomenon occurs at. I read it in a book called The Disappearing Spoon by Sam Kean and it was in the section about creating new elements and islands of stability past the current limits of the periodic table.
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