It remains conceivable that the court could avoid ruling on the question for a second time. Justice Anthony M. Kennedy, who almost certainly holds the crucial vote and has never voted to uphold an affirmative action plan, spent almost all of his time exploring whether the university should be allowed to submit more evidence to justify its use of race in accepting students.

Justice Kennedy seemed frustrated at the prospect of having to decide the case, which the court largely ducked in a previous encounter in 2013. “We’re just arguing the same case,” he said. “It’s as if nothing had happened.”

The case, Fisher v. University of Texas, No. 14-981, was brought by Abigail Fisher, a white student who says the University of Texas denied her admission in 2008 because of her race. She has since graduated from Louisiana State University.

Several of the court’s conservative justices subjected the lawyers defending the Texas plan to a barrage of skeptical questions. As usual, Justice Clarence Thomas said nothing, but he is an adamant opponent of affirmative action. Justice Scalia’s questions were particularly hostile to racial preferences, which he said could leave minority students worse off. “Most of the black scientists in this country don’t come from schools like the University of Texas,” he said. “They come from lesser schools where they do not feel that they’re being pushed ahead in classes that are too fast for them.”

Chief Justice John G. Roberts Jr. questioned the value of diversity in at least some academic settings. “What unique perspective does a minority student bring to a physics class?” he asked.