Many are single or estranged from family members and friends, and often have drug and alcohol addictions and mental health problems. They avoid the city’s traditional homeless shelters and instead take up residence below scaffolding, on subway platforms, or in any number of corners of the city to wait out freezing weather.

“The large majority of homeless New Yorkers sleeping on the streets are living with mental illness and other disabilities, and their numbers are on the rise,” said Patrick Markee, deputy executive director for advocacy for the Coalition for the Homeless.

In the Bronx, outreach workers who know the regulars from their rounds have reported seeing a couple of dozen new faces this winter as well as larger encampments under bridges and near highway ramps. Every year since 2012 in Midtown Manhattan, more homeless people have congregated late at night in pedestrian areas and public spaces, especially in warmer months, said Dan Biederman, president of the 34th Street Partnership, which manages the neighborhood.

Efforts to help homeless people underscore the scope of the problem. The new safe haven center in the Bronx is run by BronxWorks, a social services agency that also runs a 50-bed safe haven and adjoining drop-in center that has been packed every night. Scott Auwarter, BronxWorks’s assistant executive director, said that so many homeless people need a safe, warm place at night that they even curl up in chairs at the drop-in center, which has no beds but is open all the time. About 100 people a night are staying at the drop-in center, up from 60 a year ago, he said.

The city’s Department of Homeless Services plans to extend hours at more drop-in shelters. It has also expanded a network of beds in churches and community buildings that serves as an alternative to the traditional shelter system, and allows homeless people to remain in the neighborhoods where they feel most at home. This winter, the department has added 30 beds for a total of 300 around the city.

In addition, the department has increased the number of outreach workers who check on unsheltered homeless people to try to bring them in from the cold. Since July, it has extended its patrols to the subway system, which was previously monitored by the Metropolitan Transportation Authority, and sent 280 people to safe havens and other places.

Image Andre Fields, 55, sleeps at Riverside Church’s refuge for homeless people. Credit... Edwin J. Torres for The New York Times

In Greenpoint, Brooklyn, the Lutheran Church of the Messiah teamed up with a community group, Common Ground, to start an overnight respite program last month for up to 10 homeless men in its fellowship hall. The church’s pastor, the Rev. Amy Kienzle, said she saw it as an extension of the church’s mission to serve the neighborhood. Many homeless people, some of whom speak only Polish, gather daily on park benches across from the church; one man slept in the church garden in December near a heat grate.