Michael Wilson directs the production, which is scheduled to continue at the Gerald Schoenfeld Theatre through September 9.
Shepherd and Davis will replace Candice Bergen and Kerry Butler in the roles of Alice Russell and Mabel Cantwell, while Stamos will replace Eric McCormack as Senator Joseph Russell. They will all begin performances on Tuesday, July 10.
Ashley will take over for Angela Lansbury in the role of Mrs. Sue-Ellen Gamadge on Tuesday, July 24. The actress previously played the role in the 2000 Broadway revival of the play.