Election law experts say that short of a Bush-v.-Gore scenario, in which a state’s ballot count is disputed, the Supreme Court’s justices are unlikely to wade into post-election litigation.

“They’ll do everything they can to avoid resolving disputes after the election,” said Derek T. Muller, a law professor at the University of Notre Dame. “Their hand might be forced if it comes down to one very closely contested state. But my assumption is that they will prefer the political process to play out and avoid as much as possible weighing in.”

The justices did their best to stay out of the fray in 2020, when the high court batted away challenges to the results in several swing states in the days following Election Day. Lawsuits filed by former President Donald Trump and his allies challenged alleged irregularities.

However, pre-election litigation reached the high court this week in the form of two major disputes.

On Monday, Republicans asked the Supreme Court to halt Pennsylvania’s attempt to count provisional ballots in a filing that could impact thousands of votes in the critical swing state.

The Republican National Committee intervened in a lawsuit between voters who did not have provisional ballots counted for lack of a proper envelope and Butler County, Pennsylvania. A provisional ballot is cast if there is a technical issue with a mail-in ballot, such as a lack of signature or date or envelope error.

The request came on the same day that Virginia asked the justices to allow the state to purge noncitizens from its voter rolls after the Department of Justice contested the purge ahead of Election Day.

On Wednesday, the high court in a 6-3 decision did pause that lower court ruling and allowed Virginia to remove about 1,600 noncitizens from the voter rolls.

Although Virginia wasn’t thought to be in play for Mr. Trump this election year, Pennsylvania has been, as he lost the state in 2020 by roughly 1% of the vote.

Pennsylvania is viewed as the most critical swing state this cycle, worth 19 electoral votes.

“The PA case could matter if the election is Bush v. Gore-type close,” Rick Hasen, a law professor at the University of California, Los Angeles said in an email. “Beyond that, I don’t see these as major cases on the shadow docket no matter how they come out — unlikely to determine the outcome of the 2024 elections (again unless it is as close as Florida 2000).”

One of the Supreme Court’s most controversial decisions, Bush v. Gore in 2000 rested on just over 500 votes in Florida. The justices’ ruling in favor of George W. Bush to stop the recount requested by Vice President Al Gore gave the Republican nominee enough electoral votes to secure the presidency.

Mr. Bush petitioned the high court to halt a hand count ordered by Florida courts, and within two days the justices had scheduled oral arguments. They issued a decision just one day after that — a quick turnaround, as most legal battles take months to resolve.

The Supreme Court this term has room on the justices’ November docket to schedule oral arguments for any contest that would resemble the Bush v. Gore saga, should one arise. The November calendar is relatively light, as is the December docket. (Bush v. Gore was decided in December 2000.)

“At the end of last term, the justices started granting very few cases, and one theory or suspicion that I have heard articulated in different places is that they were trying to clear the deck — that they were trying to eliminate a lot of cases that would occupy them once the election begins and there is no way of knowing in advance which cases those will be,” said Josh Blackman, a professor at South Texas College of Law.