A group opposed to affirmative action in college admissions Thursday asked the Supreme Court to overturn a key precedent that allows schools to consider race when choosing an entering class.

The petition from Students for Fair Admissions was the expected next step in its long-running challenge to Harvard University’s admissions process. Colleges and universities around the country are watching a case with major ramifications for the world of competitive admissions.

In November, the U.S. Court of Appeals for the First Circuit upheld a lower court’s ruling in 2019 that Harvard does not discriminate against Asian Americans when its undergraduate college uses race and ethnicity as a factor in reviewing applicants.

Students for Fair Admissions filed suit against Harvard in 2014, alleging that the university violates civil rights law in ways that penalize Asian Americans. Harvard denied the allegations.

The group’s new petition asks the Supreme Court to overturn a 2003 ruling that allows race-conscious admissions in higher education in the interest of achieving student body diversity. That 2003 ruling in the case known as Grutter v. Bollinger, the group contends, was “grievously wrong.”

“After six and one-half years of litigation, the hundreds of Asian-American students who were unfairly and illegally rejected from Harvard because of their race may soon have this lawsuit reviewed by the U.S. Supreme Court,” the group’s president, Edward Blum, said in a statement. “It is our hope that the justices will accept this case and finally end the consideration of race and ethnicity in college admissions.”

Harvard continues to argue that creating a diverse campus community is essential to its mission.

“As earlier court decisions have confirmed, our admissions policies are consistent with Supreme Court precedent,” the university said in a statement. “We will continue to vigorously defend the right of Harvard College, and every other college and university in the nation, to seek the educational benefits that come from bringing together a diverse group of students.”

The Supreme Court upheld the limited use of race in university admissions the last time it considered the issue in 2016. In a surprise, Justice Anthony M. Kennedy said the University of Texas’s admission program complied with the 2003 Grutter precedent.

It was the first time Kennedy had ever voted for a race-conscious government program. He sided with the court’s liberals in the 4-to-3 vote. (The court was shorthanded at the time because of the death of Justice Antonin Scalia, and Justice Elena Kagan recused herself because she had previously worked on the issue in the Obama administration.)

The dissenters in the Texas case were Chief Justice John G. Roberts Jr., Justice Clarence Thomas and Justice Samuel A. Alito Jr. They have since been joined by three conservative colleagues nominated by President Donald Trump whose past rulings and writings would seem to make them sympathetic to an argument that Grutter’s time has passed.

It could be a couple of months before the court announces whether it will hear the case. If so, it would be argued in the term that begins in October.