As soon as the Tony-winning “All the Way” closed on Broadway , the playwright, Robert Schenkkan, turned his attention to the sequel.

Five years, endless rewrites and several productions later, that new play, “The Great Society,” is coming to Broadway.

The producer Jeffrey Richards announced on Thursday that he would present a 12-week run of the play, starting Sept. 6, at the Vivian Beaumont Theater (which, although located at Lincoln Center, is considered a Broadway house).

The play will star Brian Cox (“Succession”) as President Johnson, and the production will be directed by Bill Rauch, who also directed “All the Way.”