In the end, she said, she won over many of the men. “The men along the way, they were extremely jealous and competitive,” she said. “It didn’t really last that long because they saw my production, and when they did start to work for me, they realized, ‘She was not that bad.’ ”

Like many women who became senior executives, she said she rose fastest and most smoothly when she was measured by the straightforward metric of profits. “It’s really all about money,” she said. “I always had to do better than anybody else to be considered equal. I ran great restaurants, had great profits and had the most successful people working for me.”

One handicap to becoming the chief executive, she said, was her own choice not to work overseas. “I thought so many of the countries we were going into were so against women,” she said. “I thought, I don’t need that.”

But after three years in the No. 2 spot, she and her boss disagreed about strategy. She pushed hard for changes, as she said many women in her place have done. “That’s how come I’m gone,” she said.

When women act forcefully, research suggests, men are more likely to react badly. A Lean In/McKinsey & Company survey in 2016 of 132 companies and 34,000 employees found that women who negotiated for promotions were 30 percent more likely than men to be labeled intimidating, bossy or aggressive.

Another executive spent 30 years in Fortune 500 companies, rising to the C-suite, the pool from which the next chief executive may be chosen. She described her experience in detail but insisted on anonymity because she has a settlement agreement with the company and remains friendly with her former boss. She gained a reputation for finding growth where others had not, often doubling the revenue of her divisions.

She was seen as a possible successor to the chief executive, but she said she was unprepared for corporate politics at the very top. “Before heading to the C-suite, I didn’t feel I was handicapped at all,” she said, echoing conversations with many other women. But the next rungs of the ladder depend not only on results but also on prevailing in an environment where everyone is competing for a chance at the top job.