WASHINGTON — The 10th edition of the Supreme Court under Chief Justice John Roberts Jr. begins work Monday with the prospect of a monumental ruling for gay rights that could serve as a surprising legacy of an otherwise increasingly conservative court.

Whether the justices will decide the Constitution protects the right of same-sex couples to marry dominates expectations of the coming term; such a ruling would impart landmark status on a docket that so far lacks a blockbuster case.

Some say it would be a defining moment for a closely divided court that bears the chief justice’s name but is most heavily influenced by the justice in the middle — Anthony M. Kennedy, who has written the court’s most important decisions affording protection to gay Americans.

“If the court establishes a right to same-sex marriage . . . [it] will go down in history as one that was on the frontiers of establishing rights for gays and lesbians,” David Strauss, a constitutional-law scholar at the University of Chicago, said. “The rough idea would be that the Roberts court would be to the rights of gays and lesbians what the Warren court was on race issues.”

That would seem an unlikely outcome for a court that has moved to the right since Roberts joined as chief justice nine years ago. Along with his fellow George W. Bush nominee, Justice Samuel Alito Jr., Roberts has been part of a five-justice majority, including Kennedy, that has staked out conservative positions on abortion, affirmative action, campaign finance restrictions and government accommodation of religion. It is widely seen as solicitous of corporate interests.

Along with fresh questions, such as how to assess violent but perhaps hyperbolic threats made on Facebook, some of those divisive issues may return.

Challenges to a number of state laws restricting access to abortion may reach the high court in time for consideration this term. Civil rights activists fear the court accepted a housing case from Texas last week to do away with a practice that allows challenges of policies they say have a “disparate impact” on minorities even if they were passed without discriminatory intent.

There is a chance that the court will accept one of the new challenges to the Affordable Care Act, this time about federal subsidies for those who bought insurance on an exchange that was not set up by a state. Both sides agree the subsidies are crucial to making the law work.

And a court that likes to think of itself as above politics is being drawn into a number of cases that force it to settle partisan differences.

Alabama Democrats have asked the justices to find that the state’s Republican-led legislature improperly considered race during redistricting. Arizona’s Republicans are asking them to rule that voters cannot shut out elected officials by giving the job of drawing congressional districts to an independent commission.

Even before the term began, the court was asked to intervene in challenges to changes in voting laws passed by Republican legislatures in Ohio, Wisconsin and North Carolina. They ruled 5 to 4 in the Ohio case that the election can proceed under the new laws, which cut back on the number of days for early voting.

The five justices voting yes were appointed by Republican presidents; the four who would have kept the law from going into effect were appointed by Democrats.

Such decisions threaten the comity the justices were able to achieve last year by deciding narrowly some of the controversies before them and leaving underlying ideological disagreements for future cases. Largely as a result of Roberts’ attempt to find common ground, the number of unanimous rulings jumped to heights not seen in decades.

But the seams showed in a number of those pieced-together rulings, and the deep divisions on the court were most acutely displayed in the key decision of the term: that the government could not force business owners to provide contraceptive coverage for their employees if it violated the owners’ religious beliefs.

“It is a mistake to think that the court has discovered consensus,” Erwin Chemerinsky, dean of the law school at the University of California at Irvine, said. “Justice Antonin Scalia is just as conservative and Justice Ruth Bader Ginsburg is just as liberal as ever.”

Miguel Estrada, a lawyer who frequently argues before the court, wrote in a preview of the term that “the polarizing nature of much of the Court’s jurisprudence shows no sign of abating.”

It was a polarized court that only 15 months ago set the stage for what could be the ultimate decision on same-sex marriage.

Kennedy joined the liberals and wrote the majority opinion in U.S. v. Windsor, striking down part of the Defense of Marriage Act, which denied federal recognition of same-sex marriages performed where they were legal and defined marriage as only between a man and a woman.

While the decision left open the question of whether states may make such definitions, Kennedy’s reasoning convinced federal judges across the country that the next step was to find state prohibitions unconstitutional.

Same-sex couples can marry in 19 states, including Maryland, and D.C. Since Windsor, judges have ruled in favor of same-sex marriage to some degree in 16 states and three appeals courts have found a constitutional right.

Paul Clement, who defended DOMA on behalf of the House GOP leadership, said lower courts reading Windsor concluded “it’s hard to count to five votes for upholding these laws.”

The U.S. Court of Appeals for the 10th Circuit, ruling on laws in Utah and Oklahoma, and the U.S. Court of Appeals for the 4th Circuit, reviewing Virginia’s law, agreed marriage is a fundamental right that cannot be denied gay couples.

The U.S. Court of Appeals for the 7th Circuit, striking down prohibitions in Indiana and Wisconsin, said the laws discriminate on the basis of sexual orientation and the states’ justifications for them were irrational.

No appellate court has upheld a marriage prohibition, and only one federal district judge, in Louisiana, has done so. But more than 30 states and some of the nation’s biggest corporations have asked the court to settle the issue now.

Court experts say the justices will probably take time to decide which case — or cases — to accept. They could even wait until January to act and still have time for briefing, oral arguments and a decision by the end of June, when the new term ends.

“[It] depends on what Justice Kennedy decides to do,” Irving Gornstein, director of the Georgetown Law Center’s Supreme Court Institute, said. “I agree with the conventional wisdom that the justice’s legacy consists of his [gay rights] decisions … and that he will be prepared to take the final step.”

Several notable cases the court has agreed to hear this term include the following:

— Elonis v. U.S. Were Anthony Elonis’ violent Facebook rants about his wife and law enforcement true threats or more like the hyperbole of rap lyrics? He was convicted but says the government should have needed to prove he intended to carry out the actions he wrote about.

— Zivotofsky v. Kerry. This is a long-running dispute between Congress and now two presidents over the wording on passports regarding Americans born in Jerusalem. Congress passed a law saying Americans born in the city could have “Israel” listed as the place of their birth. The executive branch says that interferes with the president’s right to recognize a foreign country, and it takes no side in who controls the city.

— Holt v. Hobbs. Does a federal law that forbids prisons from imposing a burden on an inmate’s practice of religion mean that Arkansas must allow a Muslim prisoner to grow a half-inch beard?

— Young v. United Parcel Service. Does the Pregnancy Discrimination Act require a company to offer a pregnant employee an accommodation, such as an exemption from lifting heavy packages?

— Alabama Legislative Black Caucus v. Alabama and Alabama Democratic Conference v. Alabama. The groups’ charge the legislature improperly considered race in packing minority groups into several districts, thereby reducing influence in other districts. The state contends its actions were in accordance with the Voting Rights Act, which protects the creation of majority-minority districts.