The spring lineup of limited-run Broadway plays has begun to parlay box office success and awards-season love into a handful of extensions, with the limited engagement of “Gore Vidal’s The Best Man” now booking into September.“A Streetcar Named Desire,” which didn’t get much Tony attention but did see weekly sales jump notably last week, has pushed back its closing date into August, while “The Columnist,” starring Tony-nommed John Lithgow, has extended for the second time, now playing through early July. Although not the powerhouse that fellow revival “Death of a Salesman” has turned out to be, “Best Man” has consistently posted robust B.O. figures fueled by generally positive reviews and a starry cast that includes Tony-nommed thesp James Earl Jones. It’s not yet clear how many actors in the cast — which also includes Eric McCormack, John Larroquette, Angela Lansbury and Candice Bergen — will be able to stick with the show through its new closing date of Sept. 9; the production was previously set to close July 8. “Streetcar,” meanwhile, only scored a single Tony nom for costume design, but the show nonetheless saw sales rise last week in what might be an indicator of growing momentum. Production, toplined by Blair Underwood and Nicole Ari Parker, will now play through Aug. 19 rather than the originally skedded closing date of July 22. “Columnist,” part of the 2011-12 season at Gotham nonprofit Manhattan Theater Club, has seen B.O. rise steadily since Lithgow was nommed for a Tony. Production will now play through July 1.