“There’s a real opportunity to meet the needs of your mainstream consumers — your mom with kids — by bringing the chicken that they love along with the vegetable nutrition that they need,” Mr. Christianson said.

Beyond Meat and Impossible Foods are not interested in such compromises. But in some ways, the plant-based meat start-ups are beginning to resemble major food companies themselves. Beyond Meat is valued at nearly $9 billion, making it about a third the size of Tyson.

“I don’t want to collaborate with them,” Ethan Brown said. “I want to be them.”

Impossible Foods is aiming to expand to other plant-based products, like fishless fish, and make inroads in China. At times, however, the company has struggled to make the transition from start-up to major company. Over the summer, it was unable to meet the rising demand for its patties, leading to shortages at restaurants and forcing staff members to work 12-hour shifts to keep the company’s production facility in Oakland, Calif., running.

Pat Brown, the chief executive, said Impossible Foods had solved that supply-chain problem by collaborating with the OSI Group, a global food processing firm that has worked with big-name brands like McDonald’s and Starbucks. Now, Impossible is poised to quadruple its manufacturing capacity. And the days of marathon factory shifts are over.

“Everybody,” Mr. Brown said, “was happy to see that era come to an end.”