Since 2002, Sean Baker’s claim to fame was a puppet named Greg the Bunny. Co-created by fellow NYU film school alumni Spencer Chinoy and Dan Milano, the character saw iterations on IFC and Fox — while more recently, a spinoff was developed for MTV starring a foul-mouthed alcoholic stuffed ape named Warren.But Baker has long cultivated more highbrow interests. “When I was a sophomore, I (saw) a VHS tape of Eric Rohmer’s ‘Claire’s Knee,’ and that opened up a whole new world of foreign cinema,” says the director, whose acclaimed fourth feature “Starlet” opens Nov. 9 from Music Box Films. After the French New Wave, he got turned onto British Social Realists, like Ken Loach, and then American maverick John Cassavetes. Fittingly, Baker’s previous two films, 2004′s “Take Out,” about an illegal Chinese immigrant, which he co-wrote and co-directed with Tsou Shih-Ching, and 2008′s “Prince of Broadway,” about an African-American street salesman, were both nominees for the Independent Spirits’ John Cassavetes Award. Baker’s gritty New York portraits, full of hope and hopelessness, seemed to suggest a similar path for the helmer. “I thought this must be my thing: Finding different subcultures in New York City and exploring them,” he says. “But then ‘Starlet’ came out of nowhere. I never thought I’d make an L.A. movie.” Starring model Dree Hemingway, daughter of Mariel Hemingway, the film follows a young Los Angeles woman who unexpectedly strikes up a friendship with an elderly lady. Producer Ted Hope, who had been a fan of “Prince of Broadway,” stepped in with guidance and advice while Baker was trying to get the movie financed. “Sean has tremendous empathy for his characters, and the ability to extract defining behaviors that are honest and resonate deeply,” Hope says. Baker, who recently signed with ICM, says he’s ready to take the next step. “I’m sick of working on this budget level,” he says. “It’s very hard to get by. There’s no way I could have a family. I can hardly support my dog.” Baker has four projects he’s aiming to develop, with budgets ranging from $150,000 to $15 million — the latter is a Brighton Beach-set Russian-Armenian mob story, which “eventually becomes a more accessible, human drama and comedy,” he says. While Baker has been supporting himself with his TV work over the past decade, he acknowledges that gravy train is over. And while he’s developing an hourlong show in the same vein as “Breaking Bad,” he’d prefer to focus on feature films. “I’d like to get to the point where I can be more prolific and not make a film every four years,” he says.