A group opposed to Harvard’s affirmative action policy asked the Supreme Court on Thursday to take up its lawsuit challenging the use of race in higher education admissions decisions. 

The conservative-backed group Students for Fair Admissions urged the justices to hear its appeal in a suit alleging that Harvard’s policy illegally discriminates against Asian American applicants.

If the 6-3 conservative court agrees to hear the case, it could tee up a landmark showdown over whether colleges can promote on-campus diversity by considering the racial makeup of its student body.

In its petition, Students for Fair Admissions asks the court to overturn Grutter v. Bollinger, a 2003 decision in which the Supreme Court upheld the right of college admissions boards to factor in applicants’ race in order to benefit minority groups and enhance diversity.

“Grutter’s core holding — that universities can use race in admissions to pursue student-body diversity — is plainly wrong,” the petition states. The challengers say their case against Harvard’s policy gives the court an “ideal vehicle” for reevaluating its stance on affirmative action given the school’s outsize role in past rulings.

The Thursday petition comes after the lower federal courts upheld Harvard’s policy.

In 2019, following a three-week trial, a Boston-based federal judge ruled that the school’s admissions practices did not unlawfully discriminate against Asian Americans. 

Although Harvard’s policy is “not perfect,” it withstands the most stringent level of constitutional scrutiny, U.S. District Judge Allison Burroughs, an Obama appointee, wrote in her opinion. 

That decision was affirmed last November by a panel of the U.S. Court of Appeals for the 1st Circuit, prompting the appeal by the Students for Fair Admissions to the Supreme Court.

Four or more justices must agree to hear the case in order to grant review.

Harvard did not respond to a request for comment nor did attorneys representing the school.