To foster more competition, a digital agency could, for example, mandate that companies can’t discriminate against rivals that operate on their platforms. It might ban Amazon, on which many third-party merchants depend to sell their goods, from punishing a successful outside vendor by pushing it down in its search rankings. Or it might require that Apple lower its fee for app store purchases of third-party services, such as Spotify Technology SA’s music-streaming service, which competes with Apple Music.

A digital authority was also the central recommendation in Furman’s report. The U.K.’s competition authority in July said a new regulator might be needed to police the digital platforms, mirroring Furman’s recommendations. A version is under consideration in Australia, whose competition commission also issued a similar report in July.

Some American lawmakers are warming to the idea, including Senator Lindsey Graham, a South Carolina Republican and chairman of the Judiciary Committee, who is a close ally of Trump’s. “It seems that a regulatory body is the right way to go,” Graham told reporters after a hearing on technology and competition in May.

Even Facebook’s Chief Executive Officer Mark Zuckerberg has called for global regulations on data ownership by consumers, policing harmful content, protecting the integrity of elections and guarding privacy rights. Erin Egan, Facebook’s chief privacy officer, last week outlined areas where a regulator or other outside group could help improve choice and promote innovation -- two goals of antitrust enforcement.

A regulator could oversee data portability, in which consumers move their data from one social-media site to another. It could establish standards to make sure Facebook users who want to move to an alternative network can easily take their lists of friends, photos and posts with them. Congress did something similar when it passed the 1996 Telecommunications Act, which forced carriers to let consumers keep their phone numbers when switching networks.

A related idea would have digital companies pay consumers for the use of their data. California is looking into it, while Democratic Senator Mark Warner of Virginia and a Republican colleague, Josh Hawley of Missouri, back legislation that would make companies publicize the value of the data they hold. If consumers are going to own and sell their own data, a regulator would have to set up a marketplace and establish basic rules.

Facebook and Google say users can already download their data for personal use, but critics have said the process is too cumbersome, or the data that users are allowed to move is too limited, to represent true portability.

All four companies have also said they face robust competition and don’t monopolize their respective markets or block access to their platforms by competitors.

Amazon spokesman Jack Evans said the company represents 1% of global retail, including e-commerce and brick-and-mortar stores, and that it depends on third-party sellers for its success.

Apple referred to July testimony before the House antitrust panel by a company vice president who said Apple runs a fair marketplace that has allowed apps, including Spotify, to succeed, and that its own apps face tough competition.