The United Automobile Workers’ effort, with a long-elusive goal, follows its success in securing big raises in contracts with the Detroit automakers.The United Automobile Workers union announced Wednesday that it was undertaking an ambitious drive to organize plants owned by more than a dozen nonunion automakers, including Tesla and several foreign companies — a goal that has long eluded it.The move comes weeks after the U.A.W. won new contracts from General Motors, Ford Motor and Stellantis that included wage increases of 25 percent or more over four and a half years for its 146,000 members employed there.In addition to Tesla, the targets of the drive are two other electric vehicle start-ups, Lucid and Rivian, and 10 foreign-owned automakers: Toyota, Honda, Hyundai, Nissan, BMW, Mercedes-Benz, Subaru, Volkswagen, Mazda and Volvo.The U.S. plants owned by those companies employ nearly 150,000 workers in 13 states, the union said.If the organizing drive gains momentum, it could become one of the largest by the U.A.W. since its infancy in the 1930s. The union’s past efforts to organize even single plants owned by the foreign automakers, concentrated in the South, came to nought. A foothold among those companies would signal a big shift in the American auto industry, where nonunion manufacturers have long had a significant cost advantage over the Detroit automakers.The union said the organizing drive had been prompted by inquiries from several thousand workers at nonunion plants.“Workers across the country, from the West to the Midwest and especially in the South, are reaching out to join our movement and to join the U.A.W.,” the union’s president, Shawn Fain, said in a video posted on Facebook. “The money is there. The time is right.”A Honda statement cited the automaker’s “competitive wages and benefits,” adding, “We do not believe an outside party would enhance the excellent employment experience of our associates.” Subaru did not comment directly on the union drive but referred to a series of wage increases and a comprehensive benefits package.At the DealBook conference sponsored by The New York Times on Wednesday, Elon Musk, Tesla’s chief executive, said, “If Tesla gets unionized, it will be because we deserve it and we failed in some way.” He reiterated his opposition to unions, saying that “it’s not good to have an adversarial relationship” between groups within a company.Rivian and Volkswagen said they had no comment. The other companies did not immediately respond to requests for comment.On Wednesday, the U.A.W. activated websites where workers can electronically sign cards that serve as an official certification of their desire to have union representation. Earlier, at a handful of plants, the U.A.W. had already received signed cards from more than 30 percent of the work force, the threshold required under federal law for the union to move forward with a vote on unionization, a person familiar with the matter said.The union is now working to send organizers to areas around these nonunion plants to collaborate with workers at those factories, this person said.After the U.A.W. reached agreements with the Detroit automakers to raise wages, Toyota, Honda and Hyundai announced that they, too, would increase workers’ pay.Toyota has told workers that it will raise hourly rates 9 percent in January. Honda will lift wages 11 percent and Hyundai 14 percent next year. Hyundai plans to increase wages 25 percent by 2028.The U.A.W. said Wednesday that it was making a concerted effort to organize a large Toyota plant in Georgetown, Ky., that employs about 7,800 workers and produces the Camry sedan and RAV4 sport utility vehicle.U.A.W. members have long earned more than nonunion workers. At plants in the South, wages tend to start below $20 an hour and top out at less than $30. The top U.A.W. hourly wage, previously $32, climbed to more than $40 in the contracts the union signed with the three Detroit manufacturers.The U.A.W. has fallen short twice in the past decade — by narrow margins, in 2014 and 2019 — in unionization votes at a Volkswagen factory in Chattanooga, Tenn. The U.A.W. lost by a substantial margin at a Nissan plant in Canton, Miss., in 2017. Organizing efforts at other companies’ plants have petered out before coming to a vote.But after Mr. Fain became the union’s president this year, the union promised a more aggressive approach to its contract talks with the Big Three and vowed to renew efforts to widen its reach in the industry.In addition to wage gains at the Detroit companies, the U.A.W. won agreements to preserve jobs and to keep open a Stellantis plant in Illinois that had been slated to close.Arthur Wheaton, director of labor studies at Cornell University School of Industrial and Labor Relations, said the U.A.W.’s wage gains created a stronger case for joining the union.“It shows collective bargaining works and shows the U.A.W. was successful,” he said. “They can say: ‘We saved this plant. Look at what we got. You can have this, too.’”Past organizing drives were hurt because the U.A.W. had a tarnished image, Mr. Wheaton added: Many unionized plants had closed, its members had been required to accept wage and benefit cuts to help the Detroit manufacturers survive the 2009 financial crisis, and federal corruption investigations had implicated senior union officials.“A lot of the negative things about the union — a lot of that stuff has gone away now,” Mr. Wheaton said.Santul Nerkar More