He said the complaint from members of Congress was “the weirdest one” because a court ruling that would for the first time in 230 years define what constituted an emolument would also cover them. “They could be really shooting themselves in the foot,” he said.

Yet each new set of plaintiffs makes it harder for the Justice Department to defend the president on the grounds that his opponents have no legal standing to sue him, Mr. Trump’s critics said. “It puts the government in the position of saying that nobody can address this — not hotel competitors, not states, not members of Congress,” said Norman Eisen, the chairman of CREW, which started the legal efforts. “And you cannot get away with that in a rule-of-law system.”

Mr. Blumenthal, a former Connecticut attorney general, said the president’s companies did business in about 20 countries but were shrouded in secrecy, making it impossible for Congress to carry out its constitutional duty of determining whether he was receiving illegal benefits or emoluments. “The truth is we have no clue about the president’s investors,” he said in an interview with reporters Tuesday. “How much is Russian money?”

“What we are seeking first and foremost is disclosure,” he said. “We cannot consent to what we don’t know.”

In a response to the initial lawsuit, Justice Department lawyers argued that the framers of the Constitution never intended to prevent a president from owning a business or to ban ordinary, arms-length commercial transactions. They also contended that even if the president had violated the Constitution as his opponents allege, it is up to Congress to take action, not a federal court.

Mr. Trump’s defenders have said he has gone well beyond what is legally or ethically required to distance himself from his companies, which are now being run by his two adult sons.