WASHINGTON — The Supreme Court term that begins next week is already full of contentious cases, including fights over abortion and guns. But the justices still have a lot of blank space on their calendar, with four more months of arguments left to fill.

As is typical, hundreds of cases have piled up over the summer awaiting the justices’ review. Before the new term opens Monday the justices are expected to announce some additional cases they’ll hear.

Monday will be the first time in more than a year and a half the justices have heard cases in person rather than by telephone because of the coronavirus pandemic. Here are some cases the court could announce it will hear in the coming months:

ABORTION

An abortion case already on the court’s calendar for December involves Mississippi, which is asking the justices to be allowed to enforce a ban on abortion after 15 weeks of pregnancy. The Mississippi law was enacted in 2018 but was blocked after a federal court challenge.

Other abortion cases are waiting in the wings. Among the new appeals are cases from Arkansas and Missouri over their laws limiting abortions of fetuses with Down syndrome. Lower courts blocked those laws, but an appeals court upheld a similar law in Ohio.

Religious groups also want the court to weigh in on a New York regulation that requires health insurance plans to cover abortions. The regulation upheld by lower courts exempts certain religious organizations, but the groups say it is still unconstitutional.

The court could wait to act on some or all of the pending abortion cases until it resolves the Mississippi case.

GUNS

A case on the court’s calendar for November deals with the right to carry a firearm in public for self-defense. But gun owners also want the justices to take a case about a New Jersey law that bars citizens from owning firearm magazines that hold more than 10 rounds of ammunition.

The group says that magazines that hold more than 10 rounds are standard for some of the most popular handguns in America. They want the court to say that New Jersey’s law and similar bans in seven other states and the District of Columbia are unconstitutional.

Again, the court might wait to deal with the New York gun case before acting on the gun magazine case.

TRANSGENDER RIGHTS

A Catholic hospital is asking the justices to wade into the issue of transgender rights and overturn a lower court decision in favor of a transgender man who sought to have a hysterectomy. Mercy San Juan Medical Center near Sacramento declined to allow the procedure to be performed at its facility saying it was an “elective sterilization” that violated the hospital’s ethical and religious obligations.

The patient, Evan Minton, got the surgery at a different hospital. He sued under a California law that bars discrimination.

ELECTIONS

The justices could also vote to hear election law cases.

In one, District of Columbia residents want the justices to reverse a lower court ruling that they’re not entitled to voting representation in the House of Representatives because they don’t live in a state.

The Biden administration, meanwhile, wants the justices to hear a challenge to federal election law brought by Sen. Ted Cruz, R-Texas.

Cruz’s challenge involves rules about repaying a candidate for federal office who loans his or her campaign money. Under the law, a campaign can repay the candidate up to $250,000 with money collected after the election.

Cruz, a former Supreme Court clerk, loaned his campaign $260,000 as part of his successful 2018 reelection campaign in which he defeated Beto O’Rourke. The express purpose of the loan was to challenge the law.

POLICE CONDUCT

Several cases the court is weighing involve when law enforcement officers may be sued for violating people’s constitutional rights. One of the cases concerns a passenger in a vehicle who was fatally shot by police in Hayward, Calif. The driver was suspected of being drunk, and there is a dispute over whether the officer was facing a threat when he fired the fatal shot. A federal appeals court revived a suit filed by the victim’s brother, and the city is asking the justices to step in.

UNIONS

Union opponents in Washington state are challenging a public records law that allows unions, but not the general public, to obtain contact information for in-home health care workers. A federal appeals court ruled the law doesn’t violate the Constitution, but the challengers want the court to follow up on recent rulings against organized labor by taking up their case. The contact information would enable union opponents to more easily try to persuade the health care providers to stop paying union dues.

ADS ON MASS TRANSIT

The Philadelphia-area transit system is appealing a lower court ruling that would force it to display ads touting a prize-winning investigation by the Center for Investigative Reporting into racial bias in the mortgage market. The Southeastern Pennsylvania Transportation Authority refused to run the ads, saying they violated its ban on political advertising. But the federal appeals court in Philadelphia found that the policy had been applied inconsistently and held that the decision violated the rights of the news organization.