WASHINGTON — The Supreme Court on Monday added a new affirmative action case to its docket. It is already considering a major challenge to the University of Texas’ race-conscious admissions program.

The new case, Schuette v. Coalition to Defend Affirmative Action, No. 12-682, concerns a voter initiative in Michigan that banned racial preferences in admissions to the state’s public universities. In November, the United States Court of Appeals for the Sixth Circuit, in Cincinnati, ruled that the initiative, which amended the State Constitution, violated the federal Constitution’s equal protection clause.

The initiative, approved in 2006 by 58 percent of the state’s voters, prohibited discrimination or preferential treatment in public education, government contracting and public employment. Groups favoring affirmative action sued to block the part of the law concerning higher education.

The appeals court majority said the problem with the law was that it restructured the state’s political process by making it harder for disfavored minorities to press for change.