The Democratic Party, increasingly alarmed by the potential for third-party candidates to swing the election to former President Donald J. Trump, has put together a new team of lawyers aimed at tracking the threat, especially in key battleground states.

The effort comes as challengers — including the independent candidates Robert F. Kennedy Jr. and Cornel West plus groups like No Labels as well as the Green Party — have ramped up their push to qualify for states’ ballots ahead of critical deadlines in the spring and summer.

The legal offensive, led by Dana Remus, who until 2022 served as President Biden’s White House counsel, and Robert Lenhard, an outside lawyer for the party, will be aided by a communications team dedicated to countering candidates who Democrats fear could play spoiler to Mr. Biden. It amounts to a kind of legal Whac-a-Mole, a state-by-state counterinsurgency plan ahead of an election that could hinge on just a few thousand votes in swing states.

The aim “is to ensure all the candidates are playing by the rules, and to seek to hold them accountable when they are not,” Mr. Lenhard said.

Third-party candidates have haunted Democrats in recent presidential elections — Ralph Nader is widely faulted for costing Al Gore the White House in 2000, and some in the party have argued that Jill Stein, the Green Party candidate, drew votes from Hillary Clinton in 2016 in swing states she narrowly lost to Mr. Trump.

There was little third-party activity in 2020, and it’s unclear what effect the possible presence of such candidates on the ballot this year would have. But fears among Democrats are particularly acute this year, with polls suggesting that Mr. Trump’s base of support is much more fixed than Mr. Biden’s, meaning it’s possible that some of the president’s voters could be open to an alternative.

Still, it’s hard to know whether the outsider candidates, particularly Mr. Kennedy, would draw more from Mr. Trump’s or Mr. Biden’s camp. Conventional wisdom within the Democratic Party now is that any vote not for Mr. Biden benefits Mr. Trump, and there are concerns that giving people more choices on the ballot is more likely to hurt Mr. Biden.

Gaining access to the presidential ballot is a complicated and expensive process for candidates, particularly for those not affiliated with a party, even a minor one. Laws vary from state to state, with some requiring merely a fee or a few thousand signatures, and others requiring tens of thousands of signatures gathered under tight deadline pressure, along with other administrative hurdles.

State rules limiting ballot access “ensure that the people who are on the ballot have legitimate bases of support, and it’s not simply a vanity project,” Mr. Lenhard said.

Independent candidates and third-party leadership see restrictive ballot laws, and efforts to monitor and enforce them, as anti-democratic, exemplifying the kind of two-party political machinations they say they are trying to combat.

“What are ballot access barriers? They are barriers against free speech,” said Mr. Nader, who has made four third-party runs for president. He described state ballot laws in the United States as “the worst in the Western world, by orders of magnitude.”

Gauging the popularity of third-party and independent candidates is a challenge for pollsters. If they aren’t listed in a poll, their support, of course, goes uncounted. But when a poll does include them, the results tend to drastically overestimate their support, data shows.

What polling does make clear is that a sizable block of American voters are not excited about either Mr. Biden or Mr. Trump.

In recent months, Democrats have become less concerned with No Labels, the political group that had pledged to put forward a centrist presidential ticket. The group said it is on the ballot in 18 states, but it has struggled to find viable candidates.

Instead, much of Democrats’ energy — and worry — has focused on Mr. Kennedy, 70, who first challenged Mr. Biden in the primary before announcing an independent presidential bid. An environmental lawyer and a scion of one of the great American political families, Mr. Kennedy gained further prominence in recent years for his promotion of anti-vaccine falsehoods and conspiracy theories, and for his broadly anti-establishment, anti-corporate ethos. He has name recognition and a donor base.

A recent Fox News national poll put Mr. Kennedy’s support at around 13 percent, drawing about equally from both candidates. In Georgia, considered a swing state in national elections, he averages about 6 percent in recent polls, according to FiveThirtyEight’s polling averages.

Mr. Kennedy’s campaign says he is officially on the ballot in just one state, Utah, and has sufficient signatures for ballot access in New Hampshire, Hawaii and Nevada, also considered a key battleground state this year.

A super PAC backing Mr. Kennedy said it had gathered enough signatures to help get him on the ballot in Arizona, Michigan and Georgia — all swing states — as well as South Carolina. In February, the Democratic Party filed a complaint with the Federal Election Commission, accusing the PAC and the Kennedy campaign of unlawful coordination on signature-gathering efforts.

The PAC, American Values 2024, had pledged last year to spend up to $15 million on ballot-access efforts on behalf of Mr. Kennedy, but last week announced it would no longer participate in the signature-gathering process.

Tony Lyons, a co-founder of the group, said it would continue to fight the two parties “when they try to interfere with the constitutional rights of American voters who overwhelmingly want independent candidates on the ballot.”

While Mr. Lenhard’s team is involved in scrutinizing third-party contenders for possible F.E.C. violations, Democrats see ballot access as the main issue to police, and the party’s legal team has mobilized local contingents of lawyers nationwide, along with analytics, research and field teams.

Most states require independent candidates to get thousands of signatures to get on the ballot — some, like Texas and New York, require over 100,000 names.

A handful of states require a vice president on the ticket to secure ballot access.

In some states, the fastest way for independent candidates to get on the ballot is by forming a new political party.

Mr. Kennedy and his supporters have formed a party called We the People, which his campaign says will get him on the ballot in California, Delaware, Hawaii, Mississippi and North Carolina. Mr. West’s supporters have formed the Justice for All party to secure a ballot line in at least five states.

Mr. Lenhard said those new party efforts would be monitored, to ensure that “to the degree that you are seeking status as a new political party, you are actually a political party — a large group of people who believe what you believe, not simply a single candidate wanting to circumvent existing rules.”

Mr. West, for his part, has gained access to the ballot in some states through pre-existing minor parties, some of which already have guaranteed lines on the ballot. In Oregon, his name will appear as the Progressive Party candidate; in South Carolina, it’s the United Citizens Party; in Alaska, he has the line of the Aurora Party. Mr. West is on Utah’s ballot as an independent.

“I am not aware of the D.N.C. going hostile on us yet,” said Edwin DeJesus, Mr. West’s campaign’s director for ballot access. “They are probably going to surface the spoiler narrative closer to the election.”

Before becoming an independent, Mr. West was initially a candidate for the Green Party, which will name its nominee at a virtual convention in July. Ms. Stein is seeking the nomination again.

A Green Party representative, Gloria Mattera, said the party was on the ballot in 20 states and the District of Columbia, with petitions and litigation underway in others.

In February, the Green Party was deemed eligible for the ballot in Wisconsin, a state where Ms. Stein won more than 31,000 votes in 2016. That was more than the difference in votes between Ms. Clinton and Mr. Trump, who won the state.

Ms. Mattera and other third-party leaders and candidates, including Mr. Nader, dispute arguments that outsider candidates siphon votes from Democrats, saying that many people who prefer independent or alternative party candidates simply would not vote if they didn’t have that option.

They see it as a matter of providing choice.

“Our people are not going to back the incumbent,” Mr. DeJesus said. “Biden was never going to earn those votes. We are giving people a reason to go to the ballot box.”

Ruth Igielnik, Alyce McFadden and Taylor Robinson contributed reporting.