While continuing to act onstage in "The Survivor", "The Tempest", and directing a Los Angeles production of "Bent", Grant performed in TV-movies ("Kent State" 1981, "Legs" 1983) and appeared prominently in interesting if minor films including "Happy Birthday Gemini" (1980). He attracted attention opposite another new face, Kevin Costner, as the younger and more reckless of two bicycling brothers in "American Flyer" (1984). Grant would later play other gung-ho characters, both sympathetic and not, in "Bat 21" (1988) and "Air America" (1990). Similarly magnetic TV roles included Robert Kennedy in "Citizen Cohn" (1992) and a sly Nazi in "Breaking Point" (1989). He portrayed an ambitious politician in James Foley's screen version of John Grisham's "The Chamber" (1996).
Grant's 1989 role as Russell, a gay man who enters the yuppie sphere of pals on TV's acclaimed "thirtysomething", attracted considerable attention. One brief scene, showing Grant talking in bed with a man he had picked up, enraged conservatives nationwide and reportedly lost the show some of its commercial sponsorship. Grant, however, emerged unscathed, playing supporting roles in features including "Forever Young" (1992) and receiving acclaim for his role as a troubled Mormon in the Broadway production, "Angels in America: Millennium Approaches" and its companion piece "Angels in America: Perestroika" (1993-94). Grant has also written the plays, "Snakebit", which has been performed in regional theaters throughout the USA, and "Current Events".