The agencies have said that their content arms are separately run entities, and that they can’t lowball writers because they risk losing clients. WME cited what it says are hundreds of letters from clients who are uneasy with the W.G.A.’s stance.

Still, the outside investors didn’t simply hand the agencies sacks of cash for empire-building. In some cases, they also prompted changes in the way the agencies ran their business.

There was, for instance, cost-cutting — including restrictions on who could dine in fancy restaurants and stay in high-end hotels, long considered a divine right of agents. After TPG bought into Creative Artists, the agency decreed that all but its most senior agents could no longer stay at the luxurious St. Regis in New York, according to “Powerhouse,” a 2016 book about the agency. A senior agency official later said management, not TPG, was behind these initiatives.

The fund, which rose to prominence acquiring companies like Continental Airlines and J. Crew and currently manages a $100 billion portfolio that includes stakes in Uber and Airbnb, was also eager to increase the revenue generated by each employee or asset to maximize its return on investment.

At a company retreat shortly after TPG bought its initial stake in Creative Artists, a top TPG official held up the discount European airline Ryanair as an example. The official said the airline had sought to allow passengers to fly standing up, one of the Creative Artists agents recalled in “Powerhouse,” which would help it pack more people onto each flight.

Some Creative Artists agents did try to pack more passengers onto their metaphorical flights, intensifying efforts to find projects for clients and bring in more revenue.

The problem is that agents operate in a labor-intensive business and can scale themselves only so much. “The classic story is that an agent at CAA and all the others would take 200 phone calls a day,” said Hal Vogel, a consultant and author of a book on entertainment-industry economics, alluding to Hollywood lore. “But you can’t go to 1,000, 10,000. Up to a point, you can’t stretch it.”