While reduced-service clinics might not be new, Mount Sinai does seem to be trying to create an unusual level of access to medical staff at the facility. Members will be able to call doctors on their cellphones at night and on weekends, said Dr. Evan Flatow, president of Mount Sinai West. And in an expansion of existing programs, Mount Sinai will offer house calls at Hudson Yards, dispatching doctors to offices and apartments as needs arise, Dr. Flatow said.

Health insurance will cover the cost of treatment, as it does at any hospital, though Mount Sinai’s clinic, which will employ about two dozen people, will also charge fees for the above-and-beyond services. Those fees, which haven’t been set yet, could be picked up by the corporations on behalf of their employees, Dr. Flatow suggested, or possibly wrapped into a larger amenities charge for residents.

“You can give people a health club and a garage,” he said, “but to give them better health care is really pioneering.”

Still, the idea wasn’t something that occurred to Related until the company began talking to buyers at 15 Hudson Yards about what made for an ideal place to live, said Jeff T. Blau, Related’s chief executive. “They were saying they like having their doctors around the corner, and when we thought about it we realized there were no doctors around the corner, because this neighborhood didn’t exist before,” said Mr. Blau, who also serves on Mount Sinai’s board of directors.

Related’s Hudson Yards project, a $25 billion undertaking that won’t be finished until 2025, includes offices, apartment buildings, stores and parks west of Tenth Avenue, mostly on platforms built on top of active railroad tracks. The focus to date has been on commercial developments, but in the coming years, a wave of new apartments is planned.

While that is in the works, Related, among the city’s most active and successful developers, has been busy with other projects just outside the official boundaries of Hudson Yards, whose residents would also be eligible to be patients of the new Mount Sinai outpost. Those projects include One Hudson Yards, a 178-unit rental building on West 30th Street, and Abington House, a connected 312-unit rental building. Owners at 520 West 28th Street, a 39-unit condo that Related developed a few blocks away, would also be invited to become members of the Mount Sinai clinic, Mr. Blau said.