Creating superheavy elements could be done with a 3 way collision: two lighter elements and third stream of neutrons. This is probably not done because simultaneous 3 way (and greater multi-way) collisions are rare.
One place where neutron flux is extremely high is inside a detonating nuclear bomb. Some new elements were discovered in early bomb tests. Is the ban on bomb testing preventing extending the periodic table? The tricky part might be confirming the creation of a new element amidst the bomb going off: the new element might persist for a time period far too short to go in, collect samples, and do chemistry.
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