In between fielding emails from parents about his school’s plan to reopen, Bud Tosti spent Tuesday unloading 120 desks at St. Katharine of Siena School in Wayne.

“You can’t socially distance with tables,” Tosti, the Catholic elementary school’s principal, said after swapping desks into six classrooms.

As public schools across the region have increasingly moved to reopen with online-only instruction, many private schools are pressing ahead with plans to bring children back to classrooms, saying they are taking precautions and can open safely.

Some private school leaders say they are seeing heightened interest from parents seeking alternatives to their districts’ virtual learning programs, and willing to begin paying tuition — in some cases tens of thousands of dollars — to ensure their kids return to learning in a classroom.

Similar dynamics are playing out nationally as schools have been thrust into the center of the pandemic reopening debate. Private schools may have financial incentives to reopen, “because otherwise families may take their kids out of the school,” said Sean Reardon, professor of poverty and inequality in education at Stanford University — or because parents with children in public schools who want in-person classes are willing to pay.

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Yet given the need for social distancing, some private-school leaders say they don’t necessarily have space for more students. They also note that their own plans could change.

“Everybody’s looking for the best option for their child,” said John Zurcher, head of admissions at William Penn Charter School in East Falls. He said the Quaker private school, which is planning in-person instruction, has been getting an “unusually high” number of calls from parents seeking to enroll.

“We’re really full” and have been turning families away, Zurcher said. The school, where tuition ranges from $23,500 for prekindergarten to $38,650 for high school, opened last year with 976 students, its largest-ever enrollment. It expects to exceed that number this year.

Private-school enrollment has generally been trending down over the last decade, said Steve Piltch, director of the School Leadership Program at the University of Pennsylvania’s Graduate School of Education. That gives schools freedom many of their public counterparts don’t have.

“Whatever the classes were there to begin with, they were smaller than most of the public schools are,” said Piltch, a former longtime head of the Shipley School on the Main Line.

It’s also a matter of money. The Haverford School said it has spent “seven figures” on measures intended to keep the virus from spreading through the all-boys campus, from improving air filtration to hiring additional cleaning staff.

“I’m sad that every school doesn’t have the same resources … to be able to provide this option to families,” said head of school John Nagl, adding that for schools opting to stay virtual, the federal government “hasn’t given them the resources” to reopen safely.

Many school districts in Southeastern Pennsylvania have been opting to start the year virtually, as public health experts warn of potential outbreaks if in-person instruction resumes. Pennsylvania has advised schools to decide about the fall based on levels of community spread of the virus, while New Jersey Gov. Phil Murphy announced last week that schools could start the fall remotely if they show they are unable to open and meet health and safety standards.

On Friday, the Chester County Health Department recommended public and private schools in Chester and Delaware Counties open virtually through Oct. 9, citing potential increased cases “due to the end of the summer holiday.”

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Some districts that opted for online-only instruction have said they don’t have enough teachers willing to return to school buildings. Several private-school leaders said they were still talking with teachers about such staffing challenges.

“Our teachers want to be in school,” Tosti said, though “we all have some fears and anxieties.” He declined to say if any teachers requested leave due to health conditions, saying it was confidential information.

Nagl said teachers with health issues at the Haverford School would be given the chance to work remotely. “Cameras can work both ways,” said Nagl, whose school, like others, has been equipping classrooms with cameras so children opting for virtual lessons can tune in. He said it was “entirely possible” some students would come to a classroom and be taught by a teacher working from home.

Unlike public school staffers, most private-school teachers are not unionized. “There’s no question that piece matters,” Piltch said.

One exception is teachers at the 17 high schools run by the Archdiocese of Philadelphia. Rita Schwartz, head of the 500-member Association of Catholic Teachers, said the union had been involved in the reopening plans for the schools, which plan to bring students back to classrooms part time.

Schwartz said the archdiocesan school system “is trying very hard to do everything they can to make sure there’s cleaning done at all times, the teachers are safe, and that education can hopefully get as back to normal as possible with what’s going on.” Asked about teachers requesting to work remotely, she said: “It’s an option for the students. That I know.” Some teachers are concerned about returning, Schwartz said, but “haven’t made any final decision yet.”

The Independence Mission Schools, a network of 15 Catholic schools mostly in Philadelphia, decided to open virtually through September in part due to lack of willing staff. “If you lose a big portion of your teaching staff, you can’t recover,” said Bruce Robinson, CEO of the network, adding that he was unsure whether reopening could be done safely.

Charter schools, which are publicly funded but managed independently, are also making reopening decisions. In Philadelphia, 82 are opening virtually, three are offering a hybrid program, and one is still determining plans, district officials said.

While its high schools are offering a hybrid model, the archdiocese’s more than 100 elementary schools, including Tosti’s school in Wayne, are planning to bring students back five days a week, with guidelines that call for spacing desks three to six feet apart.

That distinction has become controversial in public school plans: After Bucks County instructed schools to provide at least three feet of spacing, the Pennsylvania State Education Association pushed back, calling for a six-foot minimum as recommended by state officials and the U.S. Centers for Disease Control and Prevention.

Tosti acknowledged social distancing is a challenge, but said the 400-student school is following the archdiocese’s guidelines. He noted that everyone will wear face masks — a state requirement for schools — and said teachers’ desks would be distanced from students.

While some families are reluctant about returning, others are “really happy that we’re in school five days a week,” Tosti said. The school, where tuition for one child is $5,800, is getting enrollment requests and turning down “a lot of people” for lack of space.

Some independent schools have bought tents to hold classes outside. Among them is Germantown Friends School, which is also adding portable sinks and mobile restrooms to its campus to enable more hand-washing and create more space in bathrooms, said Dana Weeks, head of school. Like others, she said the school is following health guidance.

Weeks did not yet know what the school — which is planning to bring younger students back five days a week and older students part time — would spend on the measures. “I’m sure it’s a bigger number than I even want to entertain,” she said.

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While Germantown Friends “has seen some interest” from families looking to enroll, others have left due to the virus’ toll on their finances or health, Weeks said. The school, which has offered additional financial aid due to the pandemic as others have, charges $20,500 for preschool, up to $40,350 per year for high school.

Among those who have switched to private schools is Tina Lazicki, of Cherry Hill, who sought a full-time option for her 6-year-old daughter, Juliana, after struggles with virtual learning in the spring. While many schools had wait lists, Lazicki secured a spot at Fervent Beginnings, a faith-based daycare in Voorhees that added a blended first-grade class this year.

“I know it’s a gamble and it’s a lot of money,” said Lazicki, a single mother who works two jobs as an optometry technician and manager at the Kids First Swim School in Cherry Hill, and is hoping to pick up extra hours to pay the $560-a-month tuition. “I never thought in a million years I would be sending my daughter to a private school.”

Whether any shifts from public to private schools now will have long-term effects is unclear. Reardon, of Stanford, doesn’t think so, in part because the number of families leaving the public system could be relatively small.

“When things are back to normal, I suspect people will make the same decisions they would have” before the pandemic, Reardon said.

Piltch, the Penn professor and former private-school leader, said parents who pull children from public school will be evaluating what happens in the weeks and months to come.

“And if the kids have the level of experience that those private and independent schools hope they will have,” he said, “there will be many parents who choose to keep their kids in those schools, if they can.”

Staff writer Melanie Burney contributed to this article.