SAN FRANCISCO — When John Battelle’s teenage son broke his leg at a suburban soccer game, naturally the first call his parents made was to 911. The second was to Dr. Jordan Shlain, the concierge doctor here who treats Mr. Battelle and his family.

“They’re taking him to a local hospital,” Mr. Battelle’s wife, Michelle, told Dr. Shlain as the boy rode in an ambulance to a nearby emergency room in Marin County. “No, they’re not,” Dr. Shlain instructed them. “You don’t want that leg set by an E.R. doc at a local medical center. You want it set by the head of orthopedics at a hospital in the city.”

Within minutes, the ambulance was on the Golden Gate Bridge, bound for California Pacific Medical Center, one of San Francisco’s top hospitals. Dr. Shlain was there to meet them when they arrived, and the boy was seen almost immediately by an orthopedist with decades of experience.

For Mr. Battelle, a veteran media entrepreneur, the experience convinced him that the annual fee he pays to have Dr. Shlain on call is worth it, despite his guilt over what he admits is very special treatment.

“I feel badly that I have the means to jump the line,” he said. “But when you have kids, you jump the line. You just do. If you have the money, would you not spend it for that?”

Increasingly, it is a question being asked in hospitals and doctor’s offices, especially in wealthier enclaves in places like Los Angeles, Seattle, San Francisco and New York. And just as a virtual velvet rope has risen between the wealthiest Americans and everyone else on airplanes, cruise ships and amusement parks, widening inequality is also transforming how health care is delivered.

Money has always made a big difference in the medical world: fancier rooms at hospitals, better food and access to the latest treatments and technology. Concierge practices, where patients pay several thousand dollars a year so they can quickly reach their primary care doctor, with guaranteed same-day appointments, have been around for decades.

But these aren’t the concierge doctors you’ve heard about — and that’s intentional.

Dr. Shlain’s Private Medical group does not advertise and has virtually no presence on the web, and new patients come strictly by word of mouth. But with annual fees that range from $40,000 to $80,000 (more than 10 times what conventional concierge practices charge), the suite of services goes far beyond 24-hour access or a Nespresso machine in the waiting room.

Indeed, as many Americans struggle to pay for health care — or even, with the future of the Affordable Care Act in question on Capitol Hill, face a loss of coverage — this corner of what some doctors call the medical-industrial complex is booming: boutique doctors and high-end hospital wards.

“It’s more like a family office for medicine,” Dr. Shlain said, referring to how very wealthy families can hire a team of financial professionals to manage their fortunes and assure the transmission of wealth from generation to generation.

Only in this case, they are managing health, on behalf of clients more than equipped to pay out of pocket — those for whom, as Dr. Shlain put it, “this is cheaper than the annual gardener’s bill at your mansion.”

There are rewards for the physicians themselves, of course. A successful internist in New York or San Francisco might earn $200,000 to $300,000 per year, according to Dr. Shlain, but Private Medical pays $500,000 to $700,000 annually for the right practitioner.

For patients, a limit of no more than 50 families per doctor eliminates the rushed questions and assembly-line pace of even the best primary care practices. House calls are an option for busy patients, and doctors will meet clients at their workplace or the airport if they are pressed for time.

In the event of an uncommon diagnosis, Private Medical will locate the top specialists nationally, secure appointments with them immediately and accompany the patient on the visit, even if it is on the opposite coast.

Meanwhile, for virtually everyone else, the typical wait to see a doctor is getting longer.

A survey released in March by Merritt Hawkins, a Dallas medical consulting and recruiting firm, found it takes 29 days on average to secure an appointment with a family care physician, up from 19.5 days in 2014. For some specialties, the delays are similarly long, with a 32-day wait to see a dermatologist, and a 21-day delay at the typical cardiologist’s office.

And some patients are willing to pay a lot to avoid that. MD Squared, an elite practice that charges up to $25,000 a year, opened a Silicon Valley office in 2013 and within months had a waiting list to join.

“You have no idea how much money there is here,” said Dr. Harlan Matles, who specializes in internal medicine and joined MD Squared after working at Stanford, where he treated 20 to 25 patients a day and barely had time to talk to them. “Doctors are poor here by comparison.”

Doctors as Asset Managers

Nowhere is the velvet rope in health care rising faster than here in Northern California, where newfound tech wealth, abundant medical talent and a plethora of health-conscious patients have created a medical system that has more in common with a luxury hotel than with the local clinic.

In fact, before founding Private Medical, Dr. Shlain, 50, worked as the on-call doctor at the Mandarin Oriental hotel here, an experience he said taught him about how to provide five-star service as well as good medical care.

Private Medical started 15 years ago with a single location in San Francisco, and has since opened practices in nearby Menlo Park, in 2011, and Los Angeles, in 2015. Dr. Shlain is now eyeing an expansion into New York, Seattle and Santa Monica, Calif.

The annual fee covers the cost of visits, all tests and procedures in the office, house calls and just about anything else other than hospitalization, as well as personalized annual health plans and detailed quarterly goals for each patient.

Although Private Medical provides its patients with doctors’ cellphone numbers and same-day appointments, like more conventional concierge practices do, Dr. Shlain does not like the term “concierge care.”

“When I’m at a country club or a party and people ask me what I do, I say I’m an asset manager,” Dr. Shlain explained. “When they ask what asset, I point to their body.”

“We organize health care for the entire family,” he said, sitting in his hip-but-not-too-fancy office in a nondescript building in upscale Presidio Heights. Dr. Shlain and his team will coordinate treatment for grandparents in a nursing home and care for their middle-aged children, as well as provide adolescent or pediatric medicine for the grandchildren.

For example, when a teenage patient with a history of depression or anxiety moves across the country to Boston for college, Private Medical will line up a top psychiatrist near the school beforehand so a local professional is on call in case there is a recurrence. Or if a middle-aged patient is found to have cancer, Dr. Shlain can secure an appointment in days, not weeks or months, with a specialist at MD Anderson Cancer Center in Houston or Memorial Sloan Kettering Cancer Center in New York.

“It’s not because we pay them,” he added. “It’s because we have relationships with doctors all over the country.”

‘We Can Get You In’

As with the ever more rarefied tiers of frequent-flier programs or V.I.P. floors at hotels, the appeal of MD Squared and Private Medical is about intangibles like time, access and personal attention.

“I am able to give the time and energy each patient deserves,” said Dr. Matles, the MD Squared physician in Menlo Park. “I wish I could have offered this to everyone in my old practice, but it just wasn’t feasible.”

So in addition to providing immediate access to specialists, concierge doctors also come in handy when otherwise wealthy, powerful people find themselves flummoxed by a health care system that is opaque to outsiders.

“If you need to go to Mass General, we can get you in,” Dr. Matles said. “We are connected. I don’t know if I can get you to the front of the line, but I can make it smoother. Doctors like to help other doctors.”

But for all their confidence about the advantages of their particular brand of concierge medicine, these physicians are quick to admit they struggle with the ethical issues of providing elite treatment for a wealthy few, even as tens of millions of American struggle to afford basic care.

Dr. Shlain founded a software start-up, HealthLoop, that aims to “democratize” his boutique approach by allowing patients to communicate directly with their doctors through daily digital checklists and texts.

He sees no reason that the medical world should not respond to consumer demand like any other player in the service economy. “Whenever I bump into a bleeding-heart liberal, which I am, I mention that schools, housing and food are all tiered systems,” he said. “But health care is an island of socialism in a system of tiered capitalism? Tell me how that works.”

Dr. Howard Maron, who founded MD Squared, is similarly candid about the new reality of ultra-elite medical care.

“In my old waiting room in Seattle, the C.E.O. of a company might be sitting next to a custodian from that company,” he recalled. “While I admired that egalitarian aspect of medicine, it started to appear somewhat odd. Why would people who have all their other affairs in order — legal, financial, even groundskeepers — settle for a 15-minute slot?”

It’s a fair question — but the new approach does not sit so well with veteran practitioners like Dr. Henry Jones III, one of Silicon Valley’s original concierge doctors at the Palo Alto Medical Foundation’s Encina Practice. He charges $370 a month, a fraction of what newer entrants in the area like MD Squared and Private Medical do. “It’s priced so the average person in this ZIP code can afford it,” he said.

A third-generation doctor from Boston, Dr. Jones offers a version of concierge medicine that is a way of providing more personalized service — the way doctors did when he graduated from medical school more than four decades ago — rather than delivering a different standard of care.

“Encina is like a Unesco World Heritage site — we practice medicine the way it has been traditionally practiced,” he said. “Just because you’re an Encina patient doesn’t mean you can go to the front of the line, unless you need to because of your case.”

Plusher Quarters

Not far from Dr. Jones’s office in Palo Alto, the new wing of Stanford’s hospital is taking shape. Designed by the star architect Rafael Viñoly, it will feature a rooftop garden and a glass-paneled atrium topped with a 65-foot dome. And unlike the old wing, all of the new building’s 368 rooms will be single occupancy, a crucial amenity for hospitals competing to attract elite patients from across the United States and overseas.

Stanford raised a significant portion of the project’s $2 billion cost by cultivating wealthy patients — a funding model used by university hospitals around the country, which is especially effective among the millionaires and billionaires of Silicon Valley.

Not to be outdone, Lenox Hill Hospital in New York recently hired a veteran of Louis Vuitton and Nordstrom, Joe Leggio, to create an atmosphere that would remind V.I.P. patients of visiting a luxury boutique or hotel, not a hospital. “This is something that patients asked for, and we want to go from three-star service to five-star service,” said Mr. Leggio, the hospital’s director of patient and customer experience.

In its maternity ward, the Park Avenue Suite costs $2,400 per night, twice what a deluxe suite at the Carlyle Hotel down the street commands, but that’s not a problem for well-heeled new parents. Beyoncé and Jay Z welcomed their baby, Blue Ivy, into the world at Lenox Hill, as did Chelsea Clinton and her husband, and Simon Cowell and his girlfriend.

With a separate sitting room for family members, a kitchenette and a full wardrobe closet, the suite overlooking Park Avenue is a world away from the semiprivate experience upstairs at the hospital, where families share an old-fashioned room divided by a curtain. Slightly less exalted but still private rooms in Lenox Hill’s maternity ward range from $630 to $1,700 per night.

As the stream of celebrity couples suggests, there is plenty of demand for these upscale options, crowding out traditional maternity wards. Lenox Hill is replacing some of its shared maternity rooms with private rooms, a far more profitable offering for hospitals since patients pay for them out of pocket, not through insurance plans that can bargain down rates.

Hospital executives argue that giving the well heeled extra attention is a way of keeping the lights on and providing care for ordinary middle- and even upper-middle-class patients, as reimbursements from private insurers and the federal government shrink. “I need to succeed to pay for the children we are bringing in from all over the world and treat for free,” said Dr. Angelo Acquista, a veteran pulmonologist who leads Lenox Hill’s executive health and international outreach programs.

Then there are the red blankets that some big Stanford benefactors receive when they check in as patients. For doctors and nurses, it is a quiet sign of these donors’ special status, which is also noted in their medical records.

“You don’t get better care,” Dr. Jones said. “But maybe the dean comes by, and if it’s done well, it’s done invisibly. It’s an acknowledgment of a contribution to the organization.”

Valuing Relationships

Rex Chiu, an internist with Private Medical in Menlo Park, spent more than a decade as a doctor on Stanford’s faculty. “I loved my time at Stanford, but I was spending less and less time with patients,” he said. “Fifteen or 20 minutes a year with each patient isn’t enough.”

“We all say we should get the same care, but I got sick and tired of waiting for that to happen,” he added. “I decided to go for quality, not quantity.”

Besides more money, the calmer pace of high-end concierge medicine is also a major selling point for physicians — Dr. Matles said he never made it to an event at his children’s school until he joined MD Squared. But for Dr. Sarah Greene, it wasn’t really the money or the lifestyle that led her to Private Medical.

“I really have time to think about my patients when they’re not in front of me,” said Dr. Greene, a pediatrician who joined the company’s Los Angeles practice in October. “I may spend a morning researching and emailing specialists for one patient. Before, I had to see 10 patients in a morning, and could never spend that kind of time on one case.”

Getting in the door as a new hire isn’t easy. When it comes to credentials like college, medical school and residency, Dr. Shlain said, “at least two out of the three need to be Ivy League, or Ivy League-esque.”

In many ways, today’s elite concierge physician provides the same service as the family doctor did a half-century ago for millions of Americans, except that it is reserved for the tiny sliver of the population who can pay tens of thousands of dollars annually for it.

“I didn’t know this level of care was possible,” said Trevor Traina, a serial entrepreneur here who is a patient of Dr. Shlain’s. “I have a better relationship with my veterinarian than the doctors I went to in the past.”

What about everyone else? Mr. Traina doesn’t see much future for the conventional family doctor, except for patients who go the concierge route.

“The traditional model of having a good internist is dying,” said Mr. Traina, a scion of a prominent family here that arrived with the California Gold Rush. “Even the 25-year-olds at my company either have some form of concierge doc, or they’ll just go to an H.M.O. or a walk-in clinic. No one here has a regular doctor anymore.”