Jonathan Pryce in Harold Pinter’s “The Caretaker,” Simon Callow as Shakespeare and Kevin Spacey in the Sam Mendes-helmed “Richard III” are among the offerings on tap for the spring 2012 season at the Brooklyn Academy of Music.Also on the slate are a production of ” ‘Tis Pity She’s a Whore” from Brit troupe Cheek by Jowl and a staging of “The Three Sisters” from Russia’s Maly Drama Theater. All five spring theater outings are U.S. preems. “Richard III,” which has already been seen in London at the Old Vic (where Spacey is a.d.), reps the third and final outing for the Bridge Project, the three-season team-up of BAM, the Old Vic and Mendes’ Neal Street Prods. “Richard III” is the first to star Spacey. Previous outings, all seen at BAM, include a double bill of “The Winter’s Tale” and “The Cherry Orchard” and another of “As You Like It” and “The Tempest.” Haydn Gwynne (“Billy Elliot”), Chuk Iwuji, Gemma Jones and Chandler Williams are among the troupe of Brit and American thesps who make up the cast for “Richard,” landing at BAM Jan. 10-March 4. Pryce starrer “The Caretaker,” produced by Liverpool Everyman and Playhouse with Theater Royal Bath, was initially seen in Liverpool in 2009 prior to a West End outing. Christopher Morahan helms the show, running May 3-June 17. Callow toplines “Being Shakespeare,” the solo outing that preemed in the Edinburgh Festival and went on to the West End. Actor portrays the bard in Jonathan Bate’s play, which aims to create a portrait of Shakespeare based on excerpts of soliloquies and other poetry. The Tom Cairns-helmed production runs April 4-14. Also on the bill at BAM are dance shows from Mark Morris Dance Group and Israel’s Batsheva Dance Company, as well as the annual program DanceAfrica.