Peponides new role is director, artistic development and producing.
Woffington will step down from his post in January, but will remain on the theatre’s board and executive committee.
Kite will succeed Teri Schwartz in the new year.
The renowned director and playwright will depart at the end of the 2019-20 season.
The first woman to manage the $55 million Center Theatre Group offers tips on how to raise money for innovation.
Manfredi, a former assistant managing director with the Colorado company, will begin the post in the new year.
Clowdus, who founded the company in 2009, is onto a new venture: Brian Clowdus Experiences.
Pugliese, who first joined the company in 2013, will depart at the end of the month.
Following the appointment of Russell Granet as president and CEO, a number of women have been hired or promoted to leadership positions.
After the resignation of artistic director Burgess Clark due to sexual misconduct allegations, executive director Toby Schine has also stepped down.