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Melissa McCarthy has played a wide variety of misfit characters in her films and preformed them well since winning fans in 2000 as vehemently perfectionist chef Sookie St. James on the WB drama “Gilmore Girls.” She won a best supporting actress Oscar nomination for her breakthrough role as an awkward bachelorette in “Bridesmaids,” followed by parts as a titan of industry, cops, harried moms, a spy and a Ghostbuster.

Now her quirky charisma has energized a soaring career arc. With her starring role in “Can You Ever Forgive Me?” as an author turned literary forger, McCarthy is drawing considerable speculation about her chances of making another run at the Academy Awards. In this biographical drama, she plays the late biographer, magazine journalist — and felon — Lee Israel.

Israel, who specialized in book-length portraits of bygone celebrities like actress Tallulah Bankhead and cosmetics queen Estee Lauder, wrote one bestseller but found her field out of style by the 1990s. Facing eviction from her apartment, she turned to selling antiques dealers brief typewritten letters in which she mimicked the style of literary figures like Dorothy Parker and Noël Coward and then counterfeited their signatures.

In a recent phone conversation, McCarthy discussed the appeal and challenges of making a biopic about a hard-drinking, abrasive-as-sandpaper eccentric.

While showing this kind of creative stretch into a serious role is a real change from her film and TV roles, McCarthy, 48, said it wasn’t a brave new experiment for her.

“When I was living in New York [at the beginning of her career in the early 1990s], I was really into off-Broadway theater, playing in some pretty downbeat material. I was never afraid of sober stuff,” with a special regard for no-nonsense plays by Sam Shepard and Tennessee Williams.

“Acting is about getting inside a role and keeping it real. It doesn’t matter if the point is making people laugh or moving them, you have to get them to trust you. So I would go in for all kinds of roles and always try to find the best way to connect. If you look across my career, I have probably done more drama than comedy. So Lee is an unusual person, definitely, but one I felt comfortable with.”

Distinctively unconventional characters have been McCarthy’s leaning because they offer bold acting challenges; few can forget her uncanny imitation of presidential spokesman Sean Spicer on “Saturday Night Live.” But she’s also drawn to oddballs because they’re inherently “more interesting than someone who’s perfectly turned out and cool as a cucumber. Lee is flawed and fascinating and witty. If your life is kind of out of control, the way you deal with all that chaos is more exciting than following a planned, tidy script.”

It’s a hallmark of McCarthy’s film work. She often reaches back to her roots in stand-up comedy, turning a scene into an improv experiment with dialogue out of nowhere.

“I recognize those people,” she said. “I identify with them. We’re all humans. All of us have mistakes we’ve made.”

Shared experiences

She found a kindred spirit in Israel. At age 20, McCarthy moved from the small farm town of Plainview, Ill., to New York City, where she shared a cramped apartment similar to the one her character occupies in the film. Israel was a problem drinker, and McCarthy admits to some bygone youthful indiscretions along the same lines. And like Israel, who became a forger to hold financial hard times at bay, McCarthy has a criminal past.

“Once when I was 5 years old, I went to a dime store and my dad saw me trying to swallow a Chunky bar I had stolen. My parents took me up to the register and the guy said, ‘It’s all right,’ but my mom said, ‘Oh, no, it isn’t.’ Wow. Lesson learned.”

For a decade, anyway. As a teen she was led on by a thrill-seeking friend to shoplift sweaters.

“They were Esprit, very colorful, you know? We would wrap them around our waists and walk out. Crazy.”

Since those transgressions, she promises that her life has been one act of goodness. Good karma seems to have returned the favor, giving her a memorably complex, perversely likable role to play. She wasn’t initially approached by the film’s producers. She discovered that the job was open when her husband, Ben Falcone, was cast in a supporting role as a shady bookseller.

“I read it [the script] because we share our work with each other, and I absolutely fell in love with Lee,” beginning a campaign to snatch the leading role for herself. “It was a wonderful experience. Almost miraculous in some ways. We shot the whole film in 28 days, which is nothing, and it was thrilling.”

It left her with a renewed appetite for serious work, she said, especially if it involved director Marielle Heller.

“Whatever she has planned in the future, after working with her, I’m there. I don’t have to read it, I don’t have to recognize it. Tell me where to be and that’s where I’m going.”