In 2012, Mr. Perelman sued his art dealer, Larry Gagosian, claiming he’d been repeatedly induced to spend more for works than they were worth. In 2013, Harland Clarke, another Perelman company, sued Michael Milken over a deal. Mr. Perelman said it wasn’t personal, but still. Mr. Milken was — as the former head of high yield securities at Drexel, Burnham, Lambert — largely responsible for turning Mr. Perelman into a billionaire.

Both suits were dismissed.

Less well known: Mr. Perelman is an easy crier.

It happened in the offices of MacAndrews & Forbes during a recent interview as he talked about the end of his marriage to Ms. Duff. In 1996, less than two years after she gave birth to their daughter, Caleigh, Mr. Perelman broke up with her in the back seat of a chauffeured car, while attending the Democratic National Convention.

That isn’t the part that made him cry.

After returning home, Mr. Perelman called his ex-wife, Ms. Cohen. He was staying at his Creeks property. She was at their old dive on Lily Pond Lane, which is 9.5 acres.

Mr. Perelman and Ms. Cohen were not then in a great place. In addition to the way the marriage ended, he had made plain his antipathy for the man with whom she rebounded. In retrospect, Mr. Perelman acknowledged that wasn’t necessarily fair, even if the man is the former New York senator Al D’Amato, to whom personal and professional scandals clung, as The Los Angeles Times once put it, “like a sweaty undershirt.”

“She said, ‘come over,’ and we talked pretty much all night,” Mr. Perelman said, his lips quivering, eyes welling up. “And she never said a word about me giving her a hard time. We just held one another, and I talked about what a jerk I was. After that everything was like before.”

Although not entirely. They weren’t romantically involved.

But she helped him through his epic, three-year divorce with Ms. Duff and stood beside him seven years later when his fourth marriage, to the actress Ellen Barkin, ended. (Also not well: “The last time I saw Ellen, she threw a drink in my face,” he said.)