The leaders of some of America’s biggest companies are chipping away at the long-held notion that corporate decision-making should revolve around what is best for shareholders.

The Business Roundtable on Monday changed its statement of “the purpose of a corporation.” No longer should decisions be based solely on whether they will yield higher profits for shareholders, the group said. Rather, corporate leaders should take into account “all stakeholders”—that is, employees, customers and society writ large.

It...