The principals of Seven Bucks Productions –Dwayne Johnson, Dany Garcia and Hiram Garcia – are between The Rock and a hard place.

The 12-year-old film and TV shop was one of the earliest prototypes for a modern production company built around a megastar. These were businesses created to give more control and equity to figures like Johnson and his contemporaries. But as Hollywood struggles with consolidation and a cash crunch, scaling past the big name behind the brand may be essential for their long-term survival.

Some celebrity-backed companies have chosen to move into ancillary businesses beyond the movies and shows that made an actor an A-lister. Witherspoon, for instance, has become more consequential to book publishing than anyone might have predicted when Hello Sunshine launched. And Robbie and her partners at LuckyChap haven’t just made projects for the “Barbie” actress. Guided by great taste, they’ve partnered with cutting-edge creatives...