Plettner became a member of the board of directors of Siemens-Schuckertwerke in 1959 and CEO of this company in 1962. After the merging of Siemens-Schuckertwerke with Siemens & Halske AG he was a member of the board of directors of  Siemens AG. In 1971 he was appointed CEO.
Plettner's career advancement led to his membership on the board of directors at Siemens-Schuckertwerke in 1959 and his subsequent appointment as CEO in 1962. Following the merger with Siemens & Halske AG, he became a member of the board of directors at Siemens AG, where he was eventually appointed CEO in 1971.