More than 2,100 University of Tennessee students and staff are quarantined or isolated due to Covid-19

The university had 600 active Covid-19 cases as of Monday, Chancellor Donde Plowman said during a livestream Tuesday. Among them, 592 were students, and eight were employees.

"We now have 2,112 people in quarantine or self-isolation. Of these, 1,939 are students, split nearly equally between on-campus and off-campus residence," Plowman said.

"Our case counts are going up way too fast, and we will need more drastic measures to stop the upward trajectory."

Across the country, colleges and universities have reported more than 37,000 coronavirus cases from all 50 states. And the semester has barely started.

Some campuses have already had to cancel in-person classes. Undergraduates at West Virginia University will have virtual learning through September 25 after the campus saw a coronavirus spike in just the first 1 1/2 weeks of classes, WVU announced Monday.

Towson University and North Carolina State University also moved classes online after coronavirus outbreaks, and the University of Notre Dame did the same for two weeks.

Like many campuses, the University of Tennessee is scrambling to create more quarantine or isolation space as additional students get infected.

"We have secured an additional hotel as of yesterday to use as isolation space for students living on campus who test positive," Plowman said Tuesday.

"We need more isolation spaces. This hotel is not going to be enough. And we are in the process of creating more isolation space on campus."

Other universities have implemented curfews, restrictions on visitors and even lockdowns of fraternities and sororities as Covid-19 cases rise, Plowman said.

"We are evaluating a range of options, and let me be clear: everything is on the table at this point," the chancellor said.

She expressed frustration about "fraternity leaders communicating to houses how to have parties and avoid being caught, avoid the police. Stories of a fraternity renting space off campus to have their party, crammed with lots of people in close quarters. Telling fraternity members not to get tested, or how to get tested so the results aren't shared with the university."

"I don't want to pick on any part of our campus. And the truth is the vast major of our community is working hard to do the right thing," Plowman said. "This is hard, and we appreciate everyone's efforts."

CNN has reached out to the Interfraternity Council at the University of Tennessee for comment.

Plowman said there are still ways to socialize safely -- such as meeting friends outdoors and wearing a mask.

But Plowman had a warning for those encouraging others to not get tested or to not take positive test results seriously:

"Actively working to avoid isolation and quarantine is reckless, and it will further spread this virus -- jeopardizing everyone else's opportunity for a fall semester on campus."