Another surge in homeless families is expected in the District this winter, further complicating the city’s struggle to curtail an unprecedented spike in homelessness, according to a new report.

More than 820 homeless families are predicted to seek services when the temperature dips below freezing this year, a 16 percent increase from last year.

The prediction is part of the city’s “Winter Plan,” an annual road map for how the District will fulfill its legal obligation to shelter homeless people when the weather gets cold. The plan was approved Tuesday afternoon by a coalition of city leaders, social service agencies and advocates.

(Read: District says it did all it could in Relisha Rudd case)

The plan forecasts a troubling winter and recommends that the city act quickly to find more units and buildings to house homeless families. At this rate, the plan notes, every family shelter in the city will be fully occupied by December.

Being unable to find stable housing for those families could delay the planned shutdown of the dilapidated emergency shelter on the campus of D.C. General hospital and produce an even more chaotic winter for homeless families than the previous one.

Last winter, one of the coldest in history, the District struggled to keep up with the 723 homeless families who sought shelter services.

With D.C. General full, the city began sending families to motels and hotels along New York Avenue. Those filled up, too. Then families were moved to hotels in Maryland and to city recreation centers — two policies that were eventually swatted down.

Chapman Todd, a consultant who works on the Interagency Council on Homelessness, said the city began to experience problems when families stayed in shelters longer than expected, because of difficulties finding apartments they could afford.

“For a shelter system to work, families need to move out of it so more families can move in,” Todd said.

Since the winter, city officials have tried to speed up assessments for homeless families while identifying new units and buildings to house them.

About 56 families are exiting the shelter system each month, said Kristy Greenwalt, the homelessness council’s executive director.

Shutting down D.C. General — the stated goal of city officials after the disappearance in March of 8-year-old shelter resident Relisha Rudd — would call for a rate of 100 exits per month, according to Kate Coventry, a policy analyst at the DC Fiscal Policy Institute.

At Tuesday’s meeting, the city’s family services director, Michele Williams, said the District is more prepared than it was last year to deal with the increase in homelessness. The city has tried to improve coordination between social service agencies and has held more housing fairs to assist at-risk families.

The goal is to increase the number of families enlisted in the Rapid Re-Housing program, in which the city pays the rent of individuals for up to a year to help them get back on their feet. Putting more families into the program was supposed to significantly cut costs for homeless services while improving quality of life for children by keeping them out of shelters.

But the difficulty in reaching that goal became clear this summer. The city fell short of its first benchmark — to “identify and lease” 500 units for homeless families by early July. Progress slowed, officials said, because the city had difficulty finding affordable units for families, as well as persuading families to take a chance on a program that doesn’t provide permanent housing.

Meanwhile, the Council on Homelessness charted 26 percent more families seeking services this summer than last.

Experts say the District’s increase in homelessness is a result of rising rents and a shortage of housing options for low-income and middle-class residents. Studies have estimated that it would take three minimum-wage jobs to afford the average two-bedroom apartment in the District.

“We face an enormous challenge,” said Scott McNeilly, a staff lawyer at the Washington Legal Clinic for the Homeless and a member of the council. “And if we don’t rise to the challenge, there could be catastrophic consequences.”