Add one more starry play to Broadway’s spring sked: The Lincoln Center Theater production of Christopher Durang comedy “Vanya and Sonia and Masha and Spike,” starring David Hyde Pierce and Sigourney Weaver, has booked the Golden Theater for a run that opens in March.Directed by Nicholas Martin, the show earned largely enthusiastic reviews when it opened in November at the Newhouse Theater, one of Lincoln Center’s Off Broadway venues. The production’s entire original cast will make the shift to the Rialto, with a roster of thesps that also includes Kristine Nielsen, Genevieve Angelson, Shalita Grant and Billy Magnussen. A modern-day comic riff on Chekhovian themes, “Vanya” centers on a brother (Pierce) and sister (Nielsen) whose quiet life in Pennsylvania is overturned by an unexpected visit from their movie-star sister (Weaver) and her hunky young boyfriend (Magnussen). Play joins a Rialto lineup already loaded with star-driven productions of plays, including the current “Cat on a Hot Tin Roof” starring Scarlett Johansson as well as upcoming titles including Tom Hanks topliner “Lucky Guy,” Alec Baldwin and Shia LaBeouf starrer “Orphans,” Nathan Lane outing “The Nance” and Bette Midler vehicle “I’ll Eat You Last.” Joey Parnes (“End of the Rainbow”), Larry Hirschhorn (a member of the producing team of “Peter and the Starcatcher”) and John O’Boyle produce “Vanya” in association with the McCarter Theater (in Princeton, N.J.) and LCT, the two nonprofits that first produced the play. Broadway staging beings previews March 5 ahead of a March 14 opening at the Golden.