The U.S. Supreme Court could issue far-reaching rulings in a host of blockbuster cases this term, including one asking whether federal law outlaws employment bias on the basis of sexual orientation and gender identity, and another asking whether restrictive state abortion laws are unconstitutional.

But there are several other potential big rulings that could come this term in cases that have a Massachusetts connection:

1. Challenge To Puerto Rico's Financial Board

On Tuesday, the justices heard arguments in a case challenging the authority of the federal board overseeing Puerto Rico’s debt crisis.

The Financial Oversight and Management Board was established under the Obama administration to oversee the territory’s finances, but its authority was challenged in court because the board’s eight members, all nominated by the president, were not Senate confirmed.

President Trump renominated all the original members of the board — including Carlos Garcia, the Boston-based CEO of BayBoston Managers LLC and managing partner of BayBoston Capital — and his administration and the board argue that its responsibilities are primarily local and not federal, so Senate confirmation isn’t necessary.

The Boston-based First Circuit Court of Appeals held that the board violated the Constitution’s Appointments Clause.

If the Supreme Court upholds that ruling, it could lead to the invalidation of the board’s previous actions to try to settle nearly $125 billion in bond debt and unfunded pension liabilities.

2. An Appeal On DACA

Massachusetts Attorney General Maura Healey and 16 other state attorneys general are challenging Trump’s decision to end the Obama-era Deferred Action for Childhood Arrivals program, which allowed people who were brought into the country illegally as minors to legally work, attend college, enroll in the military, and purchase health insurance, among other things.

More than 8,000 of the nation’s roughly 800,000 DACA recipients live in this state, according to the Massachusetts Immigrant and Refugee Advocacy Coalition.

The Trump administration argues that the president acted lawfully when he ended the program, which he claimed was unlawfully implemented in the first place by former President Obama.

Healey and other challengers claim Trump acted in a “arbitrary and capricious” manner in eliminating the program, and lower federal courts have agreed, ordering the White House to keep it in place.

The issue has been a focus for lawmakers from Massachusetts, including Rep. Ayanna Pressley, whose 7th Congressional District has the state’s largest immigrant population.

The Supreme Court will hear arguments in the case Nov. 12.

The justices will also soon consider whether to add two more cases with Massachusetts links to the court's docket:

3. Gun Rights Case On Tap

The justices will decide whether to take up a Second Amendment challenge to the state’s ban on so-called “copycat” assault-style weapons.

The Massachusetts-based Gun Owners' Action League and other plaintiffs challenged Healey’s 2016 interpretation of the state’s assault weapons ban to also prohibit the possession or sale of copy or duplicate assault weapons and large-capacity magazines.

In April the First Circuit — with retired Supreme Court Justice David Souter sitting on the panel — ruled in Healey’s favor, saying that her measure's burden on residents’ Second Amendment rights was only minimal, and withstands intermediate-level constitutional scrutiny.

The National Rifle Association backs the challenge to the lower court ruling.

“With 2020 presidential candidates and members of Congress encouraging the confiscation of commonly-owned firearms—like the AR-15—it is vital that the Supreme Court remind politicians that they swore an oath to uphold the Constitution, which includes our sacred Second Amendment,” Jason Ouimet, the NRA-Institute for Legislative Action's executive director, said in a statement.

If the court takes up the case, it will be its first major Second Amendment case since a 2008 case, which held that Americans have an individual right to possess firearms.

4. Court Ponders Texting Suicide Case

Michelle Carter, center, departs following a parole hearing on Sept. 19 in Natick. (Steven Senne/AP)

Justices could also decide to add to the docket an appeal by Massachusetts' Michelle Carter, who was convicted of involuntary manslaughter for encouraging her boyfriend through text messages to take his own life.

Carter’s attorneys asked the court to consider whether her conviction violates her free speech rights under the First Amendment, and her due process rights.

The state Supreme Judicial Court held that Carter’s case fell under the Supreme Court’s so-called Giboney exception, named after a 1949 case in which the court held that speech in furtherance of unlawful activity is not protected.

Carter’s attorneys disagreed and asked the nation's high court to take the case up.

“This case, which garnered extensive public attention and media coverage around the globe, is an appropriate vehicle to address these important federal constitutional questions,” her attorneys argued in their brief.

The state has until next month to reply to Carter's certiorari petition.

The National Suicide Prevention Lifeline is available 24/7 at 1-800-273-8255.