This week’s dramatic court ruling that Donald Trump’s sweeping trade tariffs, which he has used to upend global trade, were in fact illegal is the latest in a series of losses for the president’s radical agenda that are ultimately heading for a final showdown in the US supreme court.

Trump has already asked the supreme court to overturn the lower court ruling in the tariffs case. Almost certain to follow are Trump’s invocation of the Alien Enemies Act to deport Venezuelans, his hostile conflict with Harvard University and his deployment of the national guard and marines to Los Angeles. All have been deemed unlawful in lower courts.

“It’s simple: the president and his administration continue to do illegal things at an astonishing pace, and so the courts are finding that these things are illegal,” said Donald Sherman, executive director and chief counsel at Citizens for Responsibility and Ethics in Washington.

“The president is committed to pursuing his agenda regardless of whether it’s legal or not, and is seeing what he can get away with.”

The ultimate arbiter of that will be the supreme court, which is stacked 6-3 in favor of conservatives, many of whom Trump has appointed. The court has already dramatically limited the ability of lower courts to issue nationwide injunctions to pause Trump administration policies across the country.

That has not stopped them from issuing more targeted blocks. On Tuesday, a three-judge panel of the fifth US circuit court of appeals ruled in a 2-1 decision that the president had unlawfully invoked the 18th-century Alien Enemies Act to deport Venezuelan men he alleged were members of a criminal gang. Its preliminary injunction blocked the administration from removing a group of Venezuelans.

The seldom-used act gives the government expansive powers to detain and deport citizens of hostile foreign nations, but only in times of war, or during an “invasion or predatory incursion”. Circuit judge Leslie Southwick rejected the Trump administration’s claim that the Venezuelan gang Tren de Aragua had engaged in a “predatory incursion” on US soil.

“This is a critically important decision reining in the administration’s view that it can simply declare an emergency without any oversight by the courts,” said Lee Gelernt, the American Civil Liberties Union attorney who represented the Venezuelans.

The Trump administration, however, could ask the entire fifth circuit to rehear the case – and it is expected to eventually reach the supreme court.

Also on Tuesday, a federal judge found that Trump had illegally deployed thousands of military troops to Los Angeles in June, and barred the Pentagon from using national guard members and marines to perform police functions, such as arrests and crowd control.

About 300 troops are still on the streets of Los Angeles and Trump is threatening to send more to other Democratic-led cities, including Chicago and Baltimore. Last month, he deployed the national guard to Washington DC, where he has direct legal control, supposedly to crack down on violent crime, which is at a 30-year low in the city.

The judge’s order, set to take effect on 12 September, condemns Trump’s apparent goal of “creating a national police force with the president as its chief”. It was a victory for the California governor, Gavin Newsom, who sued the administration in June, arguing Trump had violated the 1878 law – the Posse Comitatus Act – prohibiting the use of US military troops in domestic law enforcement.

Newsom called Trump’s actions an “unmistakable step toward authoritarianism” and an alarming abuse of power. The administration countered that troops were protecting federal officers, not enforcing laws – but the judge disagreed, ruling the deployment illegal.

A federal judge ruled that Trump’s termination of $2.6bn in grants to Harvard University was unlawful. Photograph: Shannon Stapleton/Reuters

A day later, a different federal judge ruled that the Trump administration had unlawfully terminated about $2.6bn in grants awarded to Harvard University, and ordered it to reverse funding cuts to the prestigious Ivy League school. It marked a major legal victory for the nation’s oldest university. The judge said the administration’s actions constituted illegal retaliation after Harvard refused the White House’s demands to change its policies and governance.

In a separate case, the judge had already barred the administration from halting Harvard’s ability to enrol international students, who comprise about a quarter of its student body.

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Just as Trump used the Alien Enemies Act in the context of a wider move to deport millions of people, and used troops on US soil as part of a wider authoritarian crackdown, Harvard was another test case – this time as part of Trump’s effort to leverage federal funding to force ideological changes at American universities.

Each of the cases, Sherman said, attempt to push the boundaries of what’s allowable by “brazenly violating the law”.

“He’s attempting to do things knowing that it’s illegal, knowing it would have to go to court to be challenged,” he said. “It is monumentally stupid.”

But it also presents a significant challenge for individuals and organizations forced to sue, Sherman adds – and for the courts themselves, which must keep up with the volume of lawsuits.

“They are breaking laws that are clearly written and understood, and it’s creating strain on other institutions who are struggling to keep up.”

Now Trump has asked the supreme court to review the tariff defeat after the ruling that he had overstepped his presidential powers when he enacted punitive financial measures against almost every country. In a 7-4 ruling, the Washington DC court said that, while US law “bestows significant authority on the president to undertake a number of actions in response to a declared national emergency”, none of those actions allow for the imposition of tariffs or taxes.

The ultimate decision on many, if not all, of these cases will probably be made by the supreme court. With its rulings on presidential immunity and other key conservative opinions, Trump has “indications from the supreme court that, despite what the law says, he can do what he wants,” Sherman said.

“That has informed his approach since he’s been back in office,” he added. “He seems to be unencumbered by what the law is and what the law requires.”