It’s been said that the best time to look for a new job is while you’ve still got the old one. Brenda Braxton found that to be true, with an opportunity so custom-made for her that it had her name on it. Literally.

“I was in rehearsal for another show, ‘The Hot Mikado,’ and someone came in and said ‘Do you know that they’re auditioning for a show downstairs and looking for a ‘Brenda Braxton type?’ I said ‘Oh, really? OK, then, and went on down there,” recalls the actress over a salad at the Jupiter Resort, across the street from the Maltz Jupiter Theater, where she’s starring in “Thoroughly Modern Millie.”

“When I got to the audition, they said ‘Where have you been?’ and I said ‘Upstairs working!’”

What the producers of what would eventually become the Leiber and Stoller revue “Smokey Joes’s Cafe” got was a versatile triple threat singer-dancer-actor. But the reason the real Braxton was cast in that and in so many roles is that she’s the very model of a trouper.

“I love the work,” she confirms.

That work, which dates back to the late 1970s and includes the original productions of “Dreamgirls” and “Cats,” has been celebrated, including her Tony nominated role in “Smokey Joe’s Cafe” and her record-setting part as quick-stepping murderess Velma Kelly in “Chicago,” a role that she has played more than any other actress on Broadway.

But even with the acclaim that she’s gotten, the Bronx native, who looks so much younger than her 56 years that you literally stop to check Google because you just can’t believe it, is prouder of her longevity and ability to roll with the roles. Of being a trouper, in other words.

“The work is satisfying. I literally came to Broadway to be in the chorus, and to start there and to be where I am now, to have been Tony-nominated and a principal, I didn’t know what was going to happen. I just worked my way up,” she says.

In the Maltz production of “Thoroughly Modern Millie,” she plays Muzzy, an upbeat, “larger than life” singer played previously by Sheryl Lee Ralph and Leslie Uggams. The role “is the natural progression of African-American actresses,” she says laughing. “She’s a cross between Josephine Baker and Pearl Bailey, which I liked, and I know the choreographer and the director. And the fur coat I get to wear. Very nice.”

Braxton first appeared on Broadway at 19 in an all-black production of “Guys And Dolls” starring “Benson” star Robert Guilliame. She heard about “Dreamgirls” while dating Cleavant Derricks, who would go on to win a Tony for his role as the show’s troubled soul singer Jimmy “Thunder” Early.

She auditioned five times before getting cast, which she thinks was because of an initial reluctance to have she and Derricks in the same show because of their relationship. Her persistence, she says, was because she wanted to be a part of such a momentous show.

“Nobody was spending that kind of money for a show of that caliber — millions of dollars — on a black show. The first day I was there, and (original lead) Jennifer Holliday sang, and it was stupid how good it was,” she remembers. “She started ‘And I Am Telling You’ and everybody was crying. I mean, her voice … it started through her shoes and just went up.”

Braxton’s association with the show continued for two decades, from the original production, to touring and to the 2001 20th anniversary concert version in New York, which Andrew Kato, the Maltz’s producing artistic director, coincidentally produced.

“Brenda is always a joy to watch,” Kato says of her. “It’s an honor.”

As closely associated as she is with the play, Braxton admits to having never seen the 2006 film version that garnered Jennifer Hudson her Best Supporting Actress Oscar, because she’d heard of “artistic license” taken with some of the characters and storyline and preferred not to.

But recently, “Dreamgirls” history came full circle on the set of NBC’s Broadway-themed “Smash” when Ralph, an original “Dreamgirl,” played the stage mother of Hudson’s Broadway star character. Braxton appeared alongside Hudson, playing her character’s onstage mother in the musical she’s starring in.

“I don’t think she did know my history (with the show), and I’m shy, not the type to say anything about it. But she kept looking at me and saying ‘I can’t believe how much we look alike.’ Either way, it’s great to see the next generation making history with ‘Dreamgirls.’”