In addition to the top officials and immediate family it is required by statute to protect, the agency is also providing round-the-clock protective details to the spouses and children of Mr. Trump’s adult children, as well as to several of his top aides, including Reince Priebus, H. R. McMaster and Kellyanne Conway, at the president’s request. The numbers are likely to ease a tiny bit this summer, when former Vice President Joseph R. Biden Jr. and his wife, along with Mr. Obama’s eldest daughter, are expected to lose regular protection.

With so many of the new protectees living in New York, former Secret Service officials said the agency might eventually set up a fully staffed branch of the presidential protection division there, relocating agents from across the country.

For now, though, as it awaits a potential move to Washington by Mrs. Trump and Mr. Trump’s youngest son, Barron, the agency has elected instead to fly agents in from around the country, as it would during a campaign or for a large security event. Doing so for a routine nonelection detail is less common and means the agency is paying for hotel rooms, transportation and living expenses — at Manhattan prices — the officials said.

The agency is also renting space inside Trump Tower for offices and temporary sleeping quarters, two officials said, though the details of the transaction have not been made public.

The New York field office appears to have been particularly hard hit. Of the dozens of agents stationed there, a third are involved in protection on a given day. That has diminished for now the kind of protective intelligence, financial crime and cybercrime cases that normally make up the bulk of their work, according to a former agency official briefed on its staffing. Such investigative work is seen within the agency as crucial to not only building agents’ skills and combating crime, but also sharpening their protection abilities.

“Essentially the Secret Service is in a campaign mode all of the time right now,” said James F. Tomsheck, who left the agency in 2006 after 23 years. “It will greatly degrade the quality of life for most agents in the Secret Service, because of increased travel, protracted periods of time away from family.”