The city’s new baby boom is progressing in real time on the fourth floor of Claremont Preparatory School in the financial district, which has been wiped of its old contents to make room for the record-high number of seven kindergarten classes that it is holding this year.

“It could have been eight if we wanted to,” the school’s headmaster, Irwin Shlachter, said in a recent interview, “but we stopped.”

Mr. Shlachter said he believes Claremont’s is the largest kindergarten program of any private school in the city.

The seven classrooms are lined up in a row along a curved hallway; each opens out onto a carpeted common area known at the school as “the football.”

At the football’s point, a multicolored sign hangs from the ceiling. “KINDERGARTEN,” it says in three-dimensional block letters.

The growing lower school is posing some challenges, even for Claremont, whose building, a former bank, measures 125,000 square feet. To avoid a mosh-pit atmosphere at pickup and drop-off times, administrators this year are switching the building’s three elevators to manual and enlisting teachers to stand in the lifts, where they act as temporary elevator operators.

“Like the old Saks Fifth Avenue,” the lower school head, Henry Trevor, remarked.

The halls are more navigable during the school day. On a recent visit to the fourth floor, kindergarten teachers were taking care not to schedule overlapping bathroom trips, and succeeding. When K-410 paraded single file down the hallway from the bathroom back to class, they were interrupted only by the sounds of the sing-and-dance-a-long “We’re Going on a Bear Hunt,” which emanated from K-417.

A for-profit school operator who runs a batch of nursery and elementary schools in the city, Michael Koffler of MetSchools Inc., opened Claremont in 2005, citing a growing demand for schools as more families were staying in the city.

Enrollment was disappointing the first year. The school had hired 48 staff members, but just 54 students signed up, and some grades had just four children apiece.

Since then, the student population has soared. About 500 students now attend Claremont; 120 are kindergartners, up from 24 four years ago.

The school’s admissions director, Dana Haddad, said the school had only planned to have five kindergarten classes this year, but expanded to meet demand.

Confirming a widespread sense that there are now more $800 Bugaboo strollers in the city than there are spots in private kindergartens, this year 400 more children took the test used as an admissions screener, the ERB, than there were spots in kindergarten classes.

For Ms. Haddad, the excess translated into more than 200 families who she said came to her “in a panic.”

She said there was no reason for these families’ children to have been shut out of the admissions process: They had top-notch ERB scores; they performed well in interviews with admissions directors; their teacher reports from preschool were glowing.

“These kids had it, they had it all together,” Ms. Haddad said. “All they were missing was a spot in a school.”

So Claremont decided to scale up to fit them — or rather, some of them.

Of the families to whom she did not offer seats, Ms. Haddad said some moved to country houses; others moved to New Jersey, and one sent their child to live with a grandmother in Pennsylvania.

Mr. Shlachter, the headmaster, said families commute to Claremont from all over the city: the upper Bronx, Staten Island, north of 120th Street in Manhattan, and even, in one case, from the New Jersey suburb of East Windsor.

He said that he has never seen so many families choosing to stay in the city, rather than move to the suburbs.

“What they called a baby boomlet is really a baby boom,” Mr. Shlachter said.

School leaders said the size of the kindergarten class will also strengthen their school’s sense of community.

Mr. Shlachter said the size helps him achieve his goal of transforming Claremont away from the stereotype of a finishing school for the rich.

He said he wants Claremont to match the diversity and vibrancy of downtown Manhattan.

The more children, the more diversity, he said.

“I don’t have to look for gay and lesbian parents. I don’t have to look for grandparents raising kids,” he said. “I’ve got them.”

Ms. Haddad, a graduate of the Birch Wathen Lenox School on the Upper East Side, said the school’s relatively large size will benefit the children, giving them a broader social world than she had when she graduated with a class of just 20.

Mr. Trevor, the lower school head, may be the one who is most tested by the unexpectedly large kindergarten class.

“Before I realized how many there were, I made a promise to parents that I would learn all their names by Columbus Day,” he said the other day.

The former lower school director at the Berkeley Carroll School in Park Slope and the son of the namesake of Trevor Day School, Paul Trevor, he has experience teaching at independent schools.

But this year may prove his most challenging.

The number of names he must memorize: 370, he said.