He was 120 years old when he married Philana and had the strongest command of the power among his people. Since each Platonian's own psionic ability apparently operated on a different incompatible frequency, combining their powers to challenge Parmen's was impossible and thus his authority was unassailable. He used his powers to amuse himself by torturing others and making them do his bidding.
In 2268, the USS Enterprise visited their planet, Platonius. They found Parmen near death due to a leg wound that had become infected. Dr. McCoy was able to heal him and Parmen decided that his people needed a doctor, so he tried to force McCoy to remain on the planet. When McCoy refused, Parmen used his powers to torture Kirk, Spock, Uhura and Chapel.
McCoy determined that the local food had a substance called kironide that caused the people to develop great mental powers. After injecting the Enterprise crew with the kironide, they too developed mental powers that helped them defend themselves from Parmen and his people. Before leaving, Kirk warned Parmen that if the United Federation of Planets found that Parmen and his people had fallen back to their old ways, "there will be trouble". (TOS: "Plato's Stepchildren")