In Wisconsin, a G.O.P. elections commissioner and lawyers with ties to Republicans tried to aid attempts by Howie Hawkins, the current Green Party presidential candidate, to get on the ballot there, which were ultimately unsuccessful. In Montana, state regulators found that the Republican Party violated campaign finance laws as part of an effort to boost the Greens in five down-ballot races, including for senator and governor.

And in Western Pennsylvania, petitioners from Florida and California were brought in to gather signatures for Mr. Hawkins by an outside firm whose actions Mr. Hawkins and the party said they could not account for. Mr. Hawkins also did not make the ballot there…

Republican efforts to aid the Green Party are not new. In 2016, a billionaire backer of President Trump, Bernie Marcus, the co-founder of Home Depot, provided support to Jill Stein, the Green candidate, according to people with knowledge of the strategy, who said the effort was done with the knowledge of some officials at the Trump campaign and its chairman at the time, Paul Manafort. (Mr. Manafort was subsequently convicted of eight counts in an unrelated financial fraud trial.)