When Chief Justice William H. Rehnquist, writing for the Supreme Court majority in a landmark 1997 case, rejected a minor party’s demand that it be allowed to nominate candidates who were already on the Democratic ticket, he argued that states have a strong interest in “the political stability of the two-party system.”

Nearly 25 years later, Rehnquist’s fundamental premise is now widely in question. Signs of extreme polarization and voter unease are everywhere, from this week’s congressional hearings over one party’s baldfaced attempt to overturn a presidential election to the surging number of Americans who decline to register as either Democrats or Republicans.

Past efforts to stand up viable third parties have foundered repeatedly in the United States, however — be it because they hitch themselves to quixotic causes at the expense of more mainstream appeals, or because of the obstacles the two major parties routinely place in their path.

A new political party in New Jersey is hoping to disrupt that pattern by embracing the very technique that Justice Rehnquist scorned — fusion voting — with ambitions of taking the idea national. And while the party’s founders acknowledge that the chances of success may be low, supporters say they have identified a formula that offers greater promise than more sweeping but ultimately unworkable ideas for overhauling America’s sclerotic political system.

The party, led by a core of local Republicans, Democrats and independents alarmed by the G.O.P.’s rightward drift under former President Donald J. Trump, has given itself a name that makes its middle-of-the-road ideological positioning crystal clear: the Moderate Party.

The party’s goal is to give centrist voters more of a voice at a time when, the group’s founders say, America’s two major parties have drifted toward the political fringes. But unlike traditional third parties, the Moderate Party hopes to nudge the Democratic and Republican Parties toward the center, not replace or compete with them.

One of the party’s co-founders is Richard A. Wolfe, a partner at the law firm Fried Frank and former small-town mayor who says he is repulsed by the Republican Party’s embrace of conspiracy theories and fealty toward Mr. Trump.

“Starting around 2020, my wife and I started to feel like the Republican Party no longer represented our views,” Mr. Wolfe said in an interview. “We started to get very uncomfortable with the extremism.”

But he could not bring himself to support the Democratic Party, which he views as too beholden to left-wing economic ideas and cultural causes. Feeling politically “homeless,” Mr. Wolfe began having quiet conversations with like-minded individuals about starting a new political party and stumbled across the concept of fusion voting, he said.

Under fusion voting, multiple parties can nominate the same candidate, who then appears more than once on the ballot. Proponents say it allows voters who don’t feel comfortable with either major party to express their preferences without “wasting” votes on candidates with no hope of winning.

The practice is common in New York, which has two prominent fusion parties: the Working Families Party, which backs progressive candidates but usually aligns with Democrats; and the Conservative Party, which supports candidates on the center-right but usually aligns with Republicans. In the Connecticut governor’s race in 2010, 26,000 votes cast on the Working Families Party ballot line for Dannel P. Malloy, a Democrat, made the difference between victory and defeat.

Forty-three states, including New Jersey, prohibit fusion voting, however. The Moderate Party hopes to change that by challenging those bans in state court.

The first test case is Representative Tom Malinowski, who is favored to win the Democratic primary to continue to represent New Jersey’s Seventh Congressional District. An upscale suburban area that includes Mr. Trump’s Bedminster golf club, the district became significantly more Republican-leaning after a bipartisan redistricting commission redrew the state’s maps last year.

Mr. Malinowski’s likely Republican opponent, Tom Kean Jr., is the scion of a powerful political dynasty in New Jersey. His father, Tom Kean Sr., is a moderate former governor of the state who gained national recognition as a co-chairman of the Sept. 11 commission. Mr. Malinowski narrowly defeated the younger Mr. Kean in 2020, winning by just 5,329 votes.

New Jersey political analysts expect an even more difficult race this year for Mr. Malinowski, who carefully weighed his chances before deciding to seek a third term.

In an interview, Mr. Malinowski said that he welcomed the Moderate Party’s support.

“I think this is an answer to a question that a lot of Americans have been asking,” Mr. Malinowski said. “People in the middle of the political spectrum feel disenfranchised by parties that play to their base, particularly on the Republican side.”

Although it has been dominated by the Democratic Party in recent years, New Jersey has a history of rewarding centrist politicians. Of the state’s nearly 6.5 million registered voters, slightly over four million are registered as Democrats or Republicans, leaving 2.5 million unaffiliated with either major party.

A poll of New Jersey voters conducted in April by the Monmouth University Polling Institute found that 52 percent of adults in the state either prefer or lean toward keeping Democrats in control of Congress, while 41 percent favor putting Republicans in power.

Fusion voting was once widespread across the United States. But most state legislatures outlawed the practice after it became a popular tool of minor parties and movements during the Progressive Era, threatening the two major parties’ exclusive hold on voters.

Under Gov. Woodrow Wilson, New Jersey passed a law in 1911 expressly allowing fusion tickets. Wilson hailed the measure as putting “every process of choice in the hands of the people,” according to a contemporary New York Times account. But a decade later, New Jersey state lawmakers, alarmed by the growth of minor parties, barred candidates from appearing more than once on the same ballot.

On Tuesday, the Moderate Party submitted nominating petitions on Mr. Malinowski’s behalf to the New Jersey secretary of state, Tahesha Way, along with a memorandum and various other material laying out the case for why fusion voting should be legal. The secretary of state’s office declined a request for comment.

If, as expected, Ms. Way declines to allow Mr. Malinowski to run on the Moderate Party ticket, the party and some of its supporters plan to challenge her decision in state appeals court.

Beau Tremitiere, a lawyer at Protect Democracy, a nonprofit group that is representing a voter who intends to challenge Ms. Way’s likely ruling, said that New Jersey had strong protections for voting rights and freedom of speech, assembly and association that ought to invalidate the century-old ban on fusion tickets.

Protect Democracy became involved, Mr. Tremitiere said, because the group believes that fusion voting “can help provide a meaningful off-ramp to escalating extremism and polarization.”

The state-centric strategy could allow the party to bypass the Supreme Court, whose 1997 ruling that states have the authority to outlaw fusion tickets is considered unassailable under the federal Constitution, particularly given the court’s current conservative majority.

But the Moderate Party’s legal team plans to argue that not only has political polarization reached unsustainable levels since the 1990s, fusion voting has contributed to the stability of states like New York and Connecticut.

“It’s an uphill battle, certainly,” said Jeffrey Mongiello, a lawyer in New Jersey who has written critically about the state’s ban on fusion voting. Mr. Mongiello noted that the burden would be on the plaintiffs to demonstrate that the ban on fusion voting is unconstitutional under New Jersey law, notwithstanding the Supreme Court’s ruling.

Mr. Malinowski, a former State Department official and longtime analyst for Human Rights Watch, has been an influential voice on foreign policy during his time in the House. He was an outspoken supporter of arming Ukraine to defend itself against Russia’s invasion and sponsored a bill to seize the assets of Russian oligarchs and reallocate them to the Ukrainian government.

For now, the Moderate Party is focused on changing the law in New Jersey, with the courts being the most promising avenue. But the party’s allies, which have the backing of well-heeled national donors, have identified eight to 10 other states that have a similar combination of a favorable constitution and a potentially sympathetic Supreme Court.

The Working Families Party tried a comparable gambit in Pennsylvania in 2019, resulting in a 4-to-3 State Supreme Court decision in favor of the state’s argument that fusion voting would unleash “electoral chaos.”

Supporters of fusion voting see a model that can be used to bolster centrist voices across the country and break what they say is the “doom loop of zero-sum partisan warfare” that is endangering American democracy.

“There’s a gut-wrenching aversion among many Republicans that says, ‘I could never vote for a Democrat,’” said Lee Drutman, an analyst at the New America Foundation who wrote an expert brief in favor of the Moderate Party’s petitions. “Fusion voting allows people to express their true preferences in a way the two-party system does not.”