Pencil in three more dates on Broadway’s 2011-12 calendar, with a trio of productions — Kim Cattrall topliner “Private Lives,” Audra McDonald starrer “Porgy and Bess” and Harry Connick Jr. outing “On a Clear Day You Can See Forever” — booking Rialto theaters and dates.

Although “Private Lives,” in which Cattrall had starred last year in London, and “Porgy,” set for a stint at Boston’s A.R.T. starting in August, had both been tipped for Rialto runs, neither had locked in Gotham moves until now.

Cattrall will star in “Private Lives” with Paul Gross (“Slings and Arrows”), with both thesps following the show to Broadway following a Toronto run that begins in September. Production is helmed by Richard Eyre, who also directed the 2010 West End incarnation.

Gross did not appear in the show in London, although U.K. company members Simon Paisley Day and Caroline Olsson are set to return. Thesp Anna Madeley also is new to the production.

The 1930 Noel Coward play follows a divorced couple (Cattrall and Gross) who end up honeymooning with their respective new spouses in the same hotel. Comedy was last on the Main Stem in a 2002 outing that starred Alan Rickman and Lindsay Duncan.

Produced by Duncan C. Weldon, Paul Elliott, Theater Royal Bath, Terri and Timothy Childs, Sonia Friedman and David Mirvish, “Private Lives” begins previews Nov. 6 ahead of a Nov. 17 opening at the Music Box Theater.

The high-profile redux of “Porgy and Bess” also seemed assured an eventual Rialto outing, given the major legit names involved in retooling a well-known title that these days is more often performed in opera houses.

McDonald (“Private Practice”), Norm Lewis (“Sondheim on Sondheim”) and David Alan Greer lead the cast of “Porgy,” the 1935 musical by George and Ira Gershwin and co-lyricist-librettist DuBose Heyward. Scribe Suzan-Lori Parks (“Topdog/Underdog”) and composer Deidre Murray adapt the book and the score, respectively, while Diana Paulus (“Hair”) directs.

Tuner, under the full title “The Gershwins’ Porgy and Bess,” lands on the Main Stem in a run that begins Dec. 17 ahead of a Jan. 12 opening at the Richard Rodgers Theater, where “Bengal Tiger at the Baghdad Zoo” is set to end its limited run July 3. Jeffrey Richards and Jerry Frankel (“Hair,” upcoming play “Chinglish”) produce in association with A.R.T., where the show runs Aug. 17-Oct. 2.

Another retooled version of a pre-existing tuner, “Clear Day” had already announced its plan for a fall stint but only now has confirmed its berth at the St. James Theater, where a limited summertime run of returning revival of “Hair” will close Sept. 10.

A 1965 musical by Burton Lane and Alan Jay Lerner, “Clear Day” has been reconceived by helmer Michael Mayer (“American Idiot”) with a new book by Peter Parnell. Liza Lerner, Tom Hulce, Ira Pittelman and Broadway Across America (John Gore, Thomas B. McGrath, Beth Williams) produce the musical, which begins previews Nov. 12 prior to opening Dec. 11.

Newly minted Rialto skeds come hot on the heels of recent announcements of a trio of fall plays, including Alan Rickman topliner “Seminar,” Chicago transfer “Chinglish” and a remount of Off Broadway hit “Venus in Fur.”