NEW YORK – On a recent morning, Dr. Edward S. Goldberg, an unusually affable internist who bears the look of a scholarly Robert De Niro, sat in his office on the Upper East Side of New York and described the realities of practicing general medicine in the Manhattan of the 21st century. Goldberg, who also retains a specialty in gastroenterology, opened his practice in 1993 and accepted insurance for the first 16 years.

By 2008 his reimbursements for office visits had been, in some cases, reduced to a tenth of what they were in the previous decade, he said. Colonoscopies, which had once rendered him $1,800 per procedure, were now bringing in $350.

Because there has been so much excess in the system, and because American doctors are among the highest paid in the developed world, their complaints about diminishing returns – a strain of grievance that has intensified around the Affordable Care Act – are hardly immediate triggers of collective sympathy. Median compensation for practitioners of internal medicine was about $210,000 last year.

And yet Goldberg’s experience illustrates the difficulties primary-care physicians often face in a city where staffing and real estate costs vastly outpace those in the rest of the country. By the time Goldberg stopped taking insurance in 2009, he had become unable to deliver the level of patient service he aspired to and couldn’t afford to maintain his practice as it stood, he said.

“I really had nothing left to lose,” he said.

The health care market in New York City is sufficiently unusual that members of the affluent classes routinely question the merits of doctors who do take insurance. How could the doctor satisfied to receive a $20 co-pay also be the doctor skilled enough to know that your palm’s itch is really the early sign of something rare and disfiguring?

This psychology, along with the cost-cutting strategies pursued by insurance companies over the years, have driven the field of concierge medicine – typically, boutique general practices that charge premiums for enhanced attention. Five years ago, there were 28 concierge doctors in the New York metropolitan area, according to the group Concierge Medicine Today, which studies the field. Today, there are 124.

In recent years, some of Goldberg’s patients have made unusual requests that he has obliged. In one instance, when a patient didn’t want to be seen having a colonoscopy, Goldberg closed his office for four hours to grant her more privacy. Another requested allergy shots at home and another his accompaniment to a stressful MRI where Goldberg held the patient’s toe to supply comfort.

All of this led him and a new partner, Daniel Yadegar, a cardiologist and specialist in integrative and anti-aging medicine, to embark on a whole new kind of practice, one in which patients – and there will be no more than 400 – will pay $25,000 a year for unfettered access to the doctors. Patients will be able to call and see and text the doctors whenever they want; they will be able to receive home visits, though those will cost extra (and so will lab work). They will be able to ask their doctors to travel to them should they suspect the onset of illness – even if they’re out of the country. Various Internet moguls have already expressed interest in becoming patients of the practice, which will start next month, Goldberg said.

It is not simply that checkups will be offered and ailments tended to in the way of standard concierge practices, where the average annual fees run $1,400 to $1,700 a year nationally; the practice will take a comprehensive, methodical approach to life extension.

Yadegar envisions administering state-of-the-art screenings that use biochemical markers to identify potential predictors of cancer; consulting on limiting exposure to toxins; and networking with personal trainers. Yadegar will also offer dermatological fillers such as collagen.