Coronavirus cases in Massachusetts surpassed 1,000 on Tuesday, up from 777 Monday — the largest single-day jump yet — fueling fears that the outbreak could ultimately overwhelm local hospitals.

Tufts University President Anthony Monaco told WGBH News' Greater Boston Tuesday that colleges and universities are well-equipped to help fill the gap should it happen. That's why he advocated in a recent Boston Globe op-ed that the area's higher education institutions should step up to the plate.

“I felt it was important in listening to the needs of our hospitals to prepare our campuses as alternative treatment sites," he said. "We’ve been working with Tufts Medical Center and our cities of Medford and Somerville and other providers to consider ways which our dorms can be utilized."

Monaco said university housing, for example, could be used to house medical personnel who do not want to expose their families to the virus or for patients who might not have the illness but need low-level medical treatment, in an effort to free up hospital beds.

“Another way we can help hospitals is that their COVID-positive patients who are recovering, who have now very mild or no symptoms, could be moved to an alternative treatment site to wait out the rest of isolation,” he said.

As for other university presidents in the area, Monaco said he’s optimistic they’ll embrace the idea.

“I think most of them understand the need. They’re trying to evaluate the security and education of their current students," he said. "We’ve been offering logistics, advice and other mechanisms to help them set this up."