BOSTON — With the state’s emergency assistance shelter system expected to “imminently” hit the 7,500-family cap that Gov. Maura Healey has said it is subject to, housing vouchers are being extended to 1,200 families and Emergency Assistance Director Lt. General Scott Rice detailed other steps the state is taking and the changes it is making to prepare.

As of Monday afternoon, there were 7,332 families in emergency shelter, including 37 families newly enrolled in the last 24 hours. There were 3,633 families in traditional shelters, 3,622 families staying in hotels or motels, and 77 families in temporary emergency shelters, according to the Executive Office of Housing and Livable Communities. Once the shelter system hits 7,500 families, the governor has said, a waiting list will be established despite Massachusetts’ right-to-shelter law.

Rice, the former adjutant general of the Mass. National Guard tapped by Healey two weeks ago to lead operations “in this new phase” of the ongoing emergency shelter crisis, said the state’s incident command team has been busy preparing to deal with the reality of an at-capacity shelter system.

“We are implementing some key changes this week that will help our team assess families for eligibility and prepare to launch a waitlist when we reach our limit of 7,500 families. We are committed to ensuring that families know about resources available to them while we prioritize helping long-term shelter residents exit into more stable housing options and connecting them with work opportunities,” Rice—who has largely been out of view in the two weeks since his appointment—said in a statement Monday.

The Healey administration announced Monday afternoon that it will offer mobile vouchers to approximately 1,200 families that have been in the emergency assistance system for longer than 18 months as a way of opening up space for families newly entering the system, including the influx of migrants. The vouchers are valid for any housing unit that meets the standards of the state sanitary code and the administration said they are “among the most effective, evidence-based interventions to end family homelessness.”

While the administration got at least something out of the federal government with Monday morning’s announcement of a November work authorization clinic to be held in Middlesex County, Rice continued the administration’s drumbeat of calls for more federal help.

“The Healey-Driscoll Administration continues to call on the federal government to act to address this federal problem, especially when it comes to the need for a large-scale overflow site for families to stay until a shelter unit becomes available,” he said.

Meanwhile, a court hearing on the attempt to block the state from turning away any unhoused families or pregnant women will be heard Tuesday in Suffolk Superior Court.

Legislative leaders have been tight-lipped about whether they believe it is legal for Massachusetts—the only state in the nation with a statutory obligation to provide shelter to unhoused families and pregnant women—to turn people away from the emergency shelter system as Healey has said the state will soon begin to do.

In a statement of his own Monday afternoon, House Speaker Ron Mariano said that the House is still mulling the governor’s September request for $250 million to help prop up the shelter system but “is not considering making changes to the 1983 right-to-shelter law.”

“Any temporary policy changes would be better addressed by the Administration through the issuance of an executive order formally declaring a state of emergency, as they have real-time information regarding capacity issues and staffing shortages, and are in constant communication with local officials during this rapidly developing situation,” Mariano said.

Healey declared a state of emergency around the shelter system in August. But it is far different from the state of emergency that Gov. Charlie Baker put in place during the COVID-19 pandemic, which invoked the Civil Defense Act and public health emergency statutes to provide the governor with expanded powers. Healey’s declaration did not come in the form of an executive order, but rather as a letter to federal officials.

“The Governor is invoking her authority as Governor to address an emerging and humanitarian crisis. This is a declaration that the Governor will use all the powers granted to her to issue recommendations, directions, and orders to address the shelter crisis. It is both an alert and a call to action,” a Healey spokesperson said in August.