WASHINGTON—The head of the Federal Communications Commission is laying the groundwork for expanding the agency’s authority over broadband service, people familiar with his thinking say, a move long sought by advocates of stricter regulation of Internet-service providers.

But the plan by FCC Chairman Tom Wheeler isn’t expected to satisfy all proponents of “net neutrality”—the principle that all Internet traffic should be treated equally—because it would still allow broadband providers to cut deals with content companies for...