Princeton University, one of the world’s most selective schools, is considering what would be the second significant expansion of its undergraduate enrollment since the turn of the century.

Princeton President Christopher L. Eisgruber, who took office in July 2013, said Tuesday the Ivy League university in New Jersey is examining whether to launch another round of growth several years after its undergraduate population rose more than 10 percent.

“I am inclined to do this,” Eisgruber said during a visit to The Washington Post on Tuesday. “I think it’s important.” He said no decisions have been made. But he cited expansion plans at Yale and Stanford, two of Princeton’s peers, saying that elite private institutions can grow without sacrificing quality.

“At our level of higher education, the problem isn’t affordability,” he said. “Our students graduate with very little debt. … The problem is scarcity. And if we can do something about it, we should.”

From 2001 to 2006, federal data show, Princeton’s undergraduate enrollment averaged about 4,700. It then rose steadily, crossing 5,000 for the first time in fall 2009. In the past three years, Princeton’s undergraduate total has settled at an average of about 5,350.

Demand for admission to Princeton and other top-tier universities is huge. Princeton reported in March that it had offered admission to 6.99 percent — the university used that level of precision in a news release headline — of 27,290 applicants for the incoming class of 2019. A little more than 1,300 were projected to enroll.

An expansion could boost the entering class in future years by more than 100.

“These are tiny numbers, obviously, by comparison to the great state universities,” Eisgruber said.

Eisgruber, 53, a scholar of constitutional law, holds a bachelor’s degree in physics from Princeton and a law degree from the University of Chicago. He served as provost at Princeton from 2004 to 2013 before he was named the 20th president of a school that traces its founding to the colonial era.

One of Eisgruber’s most illustrious predecessors, Woodrow Wilson, served as Princeton’s president from 1902 to 1910 before he was elected the 28th president of the United States.

In his conversation with The Post, Eisgruber indicated that he is striving to make his top-ranked university more accessible but that he also is a fervent guardian of the traditions of a liberal arts education.

He said Princeton has diversified significantly in recent years. In 2001, he said, the share of undergraduates with family income low enough to qualify for federal Pell grants was 6 percent. The share in the class that entered last fall, he said, was 18 percent.

How far will the trend continue?

“There’s not a numerical target,” Eisgruber said. “Right now, the best-in-class institutions are slightly above 20 [percent]. … We believe that we can do more for the world if we continue to admit more students from socioeconomically disadvantaged backgrounds. And I’m not satisfied at 18 [percent]. We will continue to try to push that up.”

Many analysts in recent years have suggested that online education will “disrupt” higher education. Princeton, too, is participating in an experiment with massive open online courses, known as MOOCs, on the Web site called Coursera. It offers free online courses from name-brand universities to the world.

But Eisgruber seems somewhat skeptical of predictions of an online education revolution.

“A couple of years ago, if I were going to have a conversation with just about anybody about education and what was happening, it would all be about ‘the online,'” Eisgruber said. “The enthusiasm and the hype that existed a couple years ago has been tempered by some of the results that we’re seeing across higher education.”

He said there is evidence that completion and success rates for online education, in some cases, are disappointing. Which is not to say that technology is not changing teaching, research and learning. But Eisgruber extolled the enduring power of residential education.

“The returns on a traditional face-to-face style of education, are very, very strong,” he said.

Asked whether he believes reports of the “death” of the lecture have been exaggerated, Eisgruber replied: “Yes, I do.”

Good lectures, he said, are relatively inexpensive and can motivate students. Good online lectures, he said — meaning they have engaging and interactive qualities — are expensive and hard to produce. There is much talk these days of “flipping” classrooms — that is, giving students their lectures online and having them work on projects in class.

“It’s hard to flip a classroom effectively,” Eisgruber said. “A talking head online is something that produces rapid disengagement,” he said. Even when listening to a superb lecturer in an online format, he said, “the temptation to get up to get a cookie, or a glass of water, or to walk away from this is tremendous.”

Asked about Princeton’s recent change in its grading policy, Eisgruber said he is surprised in retrospect that the issue raised such a stir. In an effort to combat grade inflation a decade ago, Princeton declared that no more than 35 percent of grades in undergraduate courses in a given department or program should be A’s. Eisgruber supported the “grade deflation” initiative at the time.

“We need to tell students that a B-plus is not the end of the world,” he said.

But he said the initiative soon became “a subject of near-obsessive concern.” People focused on the policy as “a kind of quota.” It was said to be causing great stress among some students, leading to students claiming that it played a role in relationship breakups and other troubles. After he became president, Eisgruber asked faculty to revisit the policy. It was scrapped in 2014.

Asked whether the university has seen a surge in grade inflation since the change, Eisgruber said: “We have not. It’s only been a year.”

Last fall, the Office for Civil Rights in the U.S. Department of Education wrapped up a four-year investigation of how Princeton handles sexual violence reports. It concluded that Princeton in some respects had violated the federal anti-discrimination law known as Title IX.

Eisgruber, asked about those findings, said he would not dispute them. He said the university has overhauled its procedures to bring them into compliance with federal law. One key change: The standard for weighing evidence in sexual misconduct cases is now “preponderance of the evidence.” That translates to “more likely than not” — a lower threshold for a finding of responsibility in sexual misconduct disciplinary matters than the “clear and persuasive” standard the university had previously used.

But Eisgruber said the university must focus on prevention of assaults through programs that teach students about “bystander intervention” and how to maintain respectful relations with each other in matters such as establishing consent for sexual activity.

Students need to know, he said, “this isn’t a game. This is something very important in life and the well-being of other people.”