The rule would prohibit one base from dispatching another’s vehicles without an agreement between the two; ban a practice, known as cross-class dispatching, that blurred the line between livery and black cars; and require bases to submit trip records to the Taxi and Limousine Commission, among other changes.

The city framed the proposed changes as a protection for drivers and passengers, under circumstances that could include traffic crashes or attempts to retrieve lost property. Currently, officials said, the commission has no way to identify the driver of a vehicle dispatched by a “nonaffiliated base,” making it difficult to enforce safety and consumer-protection regulations.

The measure has the enthusiastic support of many in the livery and black-car industries, which include some of Mayor Bill de Blasio’s most generous campaign contributors. Leaders of the taxi and limousine markets, including yellow taxi operators, infused his mayoral campaign with more than $300,000 and have often resisted the expansion of Uber and its rivals. (The administration noted that it had rankled some in the taxi industry over the expansion of green cabs outside Manhattan and its plan to add a surcharge to help pay for wheelchair-accessible cabs.)

Meera Joshi, the city’s taxi commissioner, said in an interview that the rule would not necessarily restrict drivers’ options. At a hearing in the taxi commission’s headquarters in Lower Manhattan on Thursday, Ira Goldstein of the Black Car Assistance Corporation, an industry group, said that most of his members would be willing to let drivers work for another base regardless of any rule change.

“It’s not that the members are being such great guys,” he said. “They just think it’s a business model that works now.”