The Trump administration has cycled through trade law after trade law as it tries to find a sound legal basis to impose the steep tariffs on foreign products that President Trump wants.

It is poised to try yet another approach.

A global 10 percent tariff that Mr. Trump imposed in February after the Supreme Court struck down his earlier global tariffs is set to lapse at 12:01 a.m. on Friday. The administration has a new batch of tariffs ready to go to replace it, which could be announced as soon as Thursday.

In June, the administration proposed issuing tariffs on 59 countries, and the 27-nation European Union, citing their failure to pass or enforce laws banning goods made with forced labor from their countries. Those tariffs would be issued under Section 301 of the Trade Act of 1974, and set at 10 to 12.5 percent. They would apply to countries supplying more than 99 percent of U.S. imports — effectively recreating the expiring 10 percent global tariff.

More duties are likely to be on the way after that. The administration has proposed another batch of tariffs, also under Section 301, on 15 countries and the European Union to offset what the White House calls unfair practices in their manufacturing sectors.

The administration also turned to another obscure trade law earlier this week, when Mr. Trump signed orders to impose a 50 percent tariff on billions of dollars of Canadian exports. The law, the Tariff Act of 1930, also known as the Smoot-Hawley Tariff Act, was written by Congress to shield American businesses during the onset of the Great Depression, though many historians believe it actually deepened the crisis. The Section 338 provision of the act that the administration used this week had never been used to impose tariffs.

Mr. Trump has long maintained that U.S. tariffs on imports were unfairly low, and he came into office wanting to transform that system. But his efforts have been met with plenty of stops, starts and setbacks, reflecting the fact that a president’s legal authority over tariff policy is in some ways limited.

The Constitution gives power over trade to Congress, but lawmakers have written numerous laws that allow the president to issue tariffs in certain circumstances. But typically, those laws are designed to help the president address unfair trade practices in certain countries or industries, not to replace the U.S. tariff system wholesale.

Peter Harrell, a visiting scholar at Georgetown Law School, said that Mr. Trump was using Section 301, a statute designed to push another country to address an unfair trade practice, to try to impose “perpetual tariffs on almost all imports.”

“Trump is very clearly pushing to use statutes that Congress intended to address discrete trade disputes with individual countries to fundamentally rewrite the U.S. tariff regime, which is not what Congress intended these statutes to do,” he said.

The Supreme Court invalidated one of Mr. Trump’s favorite legal tools in February, when it said his use of an international emergency law to impose tariffs was unlawful and ordered roughly $160 billion in tariff revenue to be refunded. Mr. Trump had used that law to announce his “Liberation Day” tariffs on foreign countries, and to penalize Canada, Mexico and China for their real or alleged role in channeling fentanyl to the United States.

After the Supreme Court decision, Mr. Trump turned to Section 122 of the Trade Act of 1974 as a stopgap. The law allows presidents to impose a tariff to address balance of payments issues, but it has a 150-day time limit that is set to expire early Friday.

Mr. Trump’s use of Section 122 has also faced legal challenges. A group of small businesses and a coalition of states each sued the administration, claiming that the government did not satisfy the law’s strict criteria. In May, a majority of judges on a federal trade court agreed, handing down the second major tariff defeat against Mr. Trump.

The administration appealed the decision, and the courts have allowed the government to continue collecting the 10 percent tax on imports as the appeal progresses.

The provision that the administration is turning to next, Section 301, is more battle tested. Mr. Trump used it to impose tariffs on China in his first term, and his use of it has survived multiple challenges in court.

But it has never before been used in such a sweeping way, to issue tariffs on dozens of countries simultaneously. And some critics say the administration is not adhering to statute because it is using the law as a pretext to restore tariffs it has already negotiated. While Jamieson Greer, the U.S. trade representative, and other U.S. officials have said they cannot prejudge the outcome of the trade investigations, administration officials have privately reassured foreign countries that their tariff rates will end up being the same as in deals negotiated last year.

Testifying in Congress Wednesday, Mr. Greer said that the administration remained intent on imposing tariffs, regardless of the legal approach.

“The specific authorities this administration is using have changed, but the trade strategy has not,” Mr. Greer said. “We are committed to continuing to use tariffs and to negotiate deals to support the re-industrialization of our economy, protect American workers and increase their wages and shrink our trade deficit.”

Tony Romm contributed reporting.