Less than 10 minutes had passed before Daniel Diermeier, Vanderbilt University’s chancellor, told hundreds of new students what the school would not do.

The university would not divest from Israel.

It would not banish provocative speakers.

It would not issue statements in support or condemnation of Israeli or Palestinian causes.

Before the hour was up on Monday, he added that Vanderbilt would not tolerate threats, harassment or protests “disrupting the learning environment.”

This month, Vanderbilt required all first-year undergraduate students to attend mandatory meetings about the university’s approach to free speech, with the hope that clear expectations — and explanations for them — would help administrators keep order after protests rocked American campuses toward the end of the last academic year.

“The chaos on campuses is because there’s lack of clarity on these principles,” Dr. Diermeier said in an interview.

There is no guarantee that the pre-emptive, plain-spoken meetings will work. Many student activists and professors at Vanderbilt have condemned the university’s rules as suppressing their speech, and even universities with histories of hard-nosed tactics have struggled with demonstrations.

But university officials nationwide are grasping for new approaches as they brace for renewed protests over the Israel-Hamas war, along with a bitterly contested presidential election. Many administrators remain shaken by the closing weeks of the spring semester, when encampments, building occupations and clashes with the police helped lead to thousands of arrests across the country.

The strategies that are coming into public view suggest that some administrators at schools large and small have concluded that permissiveness is perilous, and that a harder line may be the best option — or perhaps just the one least likely to invite blowback from elected officials and donors who have demanded that universities take stronger action against protesters.

University presidents used summer break to huddle with police commanders, lawyers, trustees and other administrators to rewrite rules, tighten protest zones, and weigh possible concessions to maintain, or restore, order. Many have studied universities that temporarily defused tensions by striking deals with protesters.

But so far, universities are signaling little overt interest in negotiations.

On Monday, the University of California’s president, Michael V. Drake, told campus chancellors to ensure that their policies included bans on unapproved encampments and “masking to conceal identity.” Columbia University, where contentious protests helped drive Nemat Shafik from her 13-month-old presidency on Aug. 14, is limiting campus access. Northwestern University said that students would receive “mandatory trainings on antisemitism and other forms of hate,” with more policy changes coming.

“The question is how do we get more consistent in the way we respond to these issues — and clearer about what the rules are and what the tiered responses will be,” said Richard K. Lyons, the new chancellor at the University of California, Berkeley, a campus with one of the nation’s most robust records of protest. Dr. Lyons estimated that planning for demonstrations had consumed up to 15 percent of the summer for top administrators at Berkeley.

Some universities are saying little, for now, about their playbooks. For example, the University of Texas at Austin, where the authorities made more than 100 arrests in the spring, did not respond to inquiries. And a spokeswoman for Emory University, where administrators provoked fury in April by swiftly ordering the removal of an encampment, said the school in Atlanta had no “updates to share.”

A series of recent court rulings, as well as investigations from Capitol Hill and the Department of Education, have created pressure on universities. A federal judge issued a preliminary injunction this month that said the University of California, Los Angeles, could not allow protesters to block Jewish students from campus facilities. (U.C.L.A. objected to the court telling it how to manage demonstrations. The court’s order, the university said, could “hamstring our ability to respond to events on the ground.”)

And university officials in Texas have scrambled in recent months to comply with Gov. Greg Abbott’s executive order to “review and update free speech policies to address the sharp rise in antisemitic speech and acts on university campuses.” A federal lawsuit challenging the order, which Mr. Abbott issued in March, is pending.

Even as some universities have prepared more rigorous rules and procedures, it remains to be seen how strongly or consistently they will be enforced. The lasting consequences of defiance are also murky. Officials nationwide ultimately dropped many of the criminal charges that protesters faced after the spring demonstrations, and school discipline is still pending for many students. Suspensions have often been lifted in the meantime.

Vanderbilt, which is in Nashville, did not experience the scale of pandemonium that some other universities did. But with about 13,000 students, there have been tensions, including a sit-in that led to a handful of arrests.

In March, university administrators, citing a possible risk to Vanderbilt’s government contracts, blocked a vote to align student government spending with the boycott, divestment and sanctions movement against Israel. Students and administrators have also bickered over the distribution of fliers and a meeting room reservation by the campus’s chapter of Students for Justice in Palestine.

The S.J.P. branch did not respond to an interview request, but the chapter and its allies have spent months warning against university tactics they saw as stifling. Last semester, a group of Vanderbilt divinity students invoked the university’s 1960 expulsion of the civil rights leader James M. Lawson Jr. and declared that “protest is once again facing Vanderbilt’s repressive and unjust reactions, all in the name of a ‘principled neutrality’ which favors the care and needs of certain students over others.”

Separately, Palestine Legal, a civil rights group, sent the university a cease-and-desist letter in March, accusing the school of arbitrarily restricting student speech and protest, which it said was “incongruous with Vanderbilt’s commitment to freedom of expression.”

Even without protests that commanded the national spotlight, Dr. Diermeier said in the interview that he had concluded over the summer that Vanderbilt needed to reinforce and explain its longstanding ethos of open inquiry and institutional neutrality, which means avoiding taking stands on debates that do not directly affect university operations.

“People are not always clear what the principles are, and they’re not always clear for the reasons for it,” said Dr. Diermeier, a former provost of the University of Chicago, where incoming students are told that freedom of expression is “an essential element of the university’s culture.”

The University of Chicago’s own experience this year suggests that even those deeply held principles do not always prevent turmoil. In May, the university brought in the police to remove an encampment that violated its policy barring unapproved tents.

Dr. Diermeier framed the sessions at Vanderbilt as gatherings intended to develop a common understanding.

“If you join a community that is governed by a certain set of rules, you want to know what they are, you want to discuss them, you want to be clear about them,” he said. “We’re not forcing anybody to be members of this community.”

Bruce Barry, a professor of management who has been on Vanderbilt’s faculty since 1991, said he saw merit to orienting new students to the university’s principles. But Dr. Barry, a former president of the American Civil Liberties Union of Tennessee who is married to a Democratic candidate for Congress, said he would worry if university leaders were deliberately “sending a message that your protest activities occur on a very thin edge of compliance.”

He noted that Dr. Diermeier’s administration hardly seemed to hesitate to discipline some students in the spring.

Some of the campus’s newest residents said they welcomed the mandatory gatherings.

Shayna Mehta, a first-year student from New Jersey, said she thought the university’s early efforts to detail policies “will make people more mindful about protests and the decisions they’re making.”

On Monday, after new students filled Langford Auditorium, there were subtle signs of discomfort with the university’s policies, particularly around its $10 billion endowment. Barrie Barto, the editor in chief of the campus newspaper, The Vanderbilt Hustler, moderated two onstage discussions with the chancellor and afterward estimated that about a quarter of the submitted questions were related to divestment. Others prodded Dr. Diermeier about how to discern the line between permitted protests and disruptions that might lead to discipline.

But as the chancellor answered questions, he faced more sleeping students (a handful, including one in the front row) than vocal protesters (none).

Anemona Hartocollis contributed reporting from New York.