A lawsuit challenging Harvard University’s admissions practices is playing out in a federal courtroom in Boston, with the trial starting Monday. But the dispute may wind up before the Supreme Court, which, now with five conservative justices, could drastically alter the future of affirmative action in college admissions.

The lawsuit, filed by the group Students for Fair Admissions, claims that Harvard engages in “racial balancing” and discriminates against Asian-American students applying to the elite school in violation of federal civil rights law. Asian-Americans, the plaintiffs contend, are held to a higher standard for admission than students of other races.

The case currently sits before Judge Allison Burroughs of the federal district court in Boston, and the trial will likely last last three weeks. An appeal to the 1st U.S. Circuit Court of Appeals, based in Boston, is expected once Burroughs issues her ruling.

If Students for Fair Admissions loses, court watchers anticipate the group will petition the Supreme Court to review the lower court’s ruling, though it could be several years before the justices consider the case, if they agree to do so.

The dispute over Harvard’s admissions could present the first opportunity for the Supreme Court, now with a conservative majority, to weigh in on the broader issue of affirmative action since 2016, when the high court heard a case challenging the University of Texas’s admissions practices for a second time after sending it back to the lower courts in 2013.

Then, the court included Justice Anthony Kennedy, long considered to be the swing vote. Kennedy sided with the court’s liberal justices in upholding Texas’s affirmative action practices.

But Justice Brett Kavanaugh’s confirmation by the Senate this month cemented a conservative majority on the high court, throwing the future of affirmative action into question.

“This is one of the hot-button issues where replacing Kennedy with Kavanaugh does make a difference,” said Ilya Shapiro, a senior fellow at the Cato Institute.

Kavanaugh is a “strong originalist and textualist," and thus is “going to be against the use of racial preferences,” Shapiro added.

While Kavanaugh’s presence on the high court could change the outcome of future affirmative action cases before the justices, Chief Justice John Roberts also plays a crucial role.

“John Roberts is the key both in result and in terms of if they take it,” Shapiro said. “In this issue, unlike others, he’s ready to go. Over a decade ago, he wrote that the only way to stop discriminating on race is to stop discriminating on race. I think with Kennedy having gone the other way in Fisher and Roberts having been in strong dissent, I think the court will be ready.”

The case dates back to 2014, when Students for Fair Admissions filed its lawsuit claiming Harvard effectively sets quotas on the number of Asian-American applicants it admits. The group is led by Edward Blum, a conservative lawyer who spearheaded the challenge to the University of Texas’s affirmative action practices.

In that case, Abigail Fisher, a white student denied admission to the University of Texas, said the school unconstitutionally used race as a consideration in the admissions process. The Supreme Court ruled in favor of the University of Texas in a 4-3 decision in 2016, which marked the last time the high court heard a case challenging the use of race in the college admissions process.

Unlike in Fisher’s case, the Asian-American students suing Harvard will remain anonymous.

Harvard denies the admissions process discriminates against Asian-Americans. In a letter to the Harvard community last week Lawrence Bacow, the university’s president, noted that the Supreme Court has heralded Harvard’s admissions process before and affirmed that race can be one of many factors taken into consideration.

“I want all of you to know that each Harvard College student is admitted affirmatively,” Bacow wrote. “Each student brings something special to our community and contributes to our rich learning environment in a way that is unique. Harvard would be a dull place — and not likely achieve the educational aspirations we have for our students — if we shared the same backgrounds, interests, experiences, and expectations for ourselves.”

Burroughs could issue a narrow ruling addressing only Harvard’s practices or issue one that is broader. But the case is expected to shed light on the elite school’s secretive admissions practices. “It’s opening up that black box that is an item of true curiosity and legal significance,” Shapiro said.

While the Harvard case could provoke review by the Supreme Court on the constitutionality of affirmative action, a lawyer for Students for Fair Admissions said during opening statements Monday that affirmative action in college admissions “is not on trial here.”

“This trial is about what Harvard has done and is doing to Asian-American applicants,” Adam Mortara said, according to reports, “and how far Harvard has gone in its zeal to use race in the admissions process.”