Besides the continuing criminal inquiry into Russia’s influence over the presidential election, an actress in pornographic films, a former Playboy model and a onetime contestant on “The Apprentice” have filed civil lawsuits over their alleged relationships with Mr. Trump before he became president.

The emoluments case raises basic questions that have never been litigated. Even the specific definition of an emolument is unclear. During a January court hearing, Judge Messitte seemed to acknowledge that the case would ultimately be decided by a higher court than his.

Although the president’s critics are hoping that the judge will allow the plaintiffs to scrutinize the Trump Organization’s financial records, perhaps even including the president’s tax returns, it was not clear from Wednesday’s opinion whether the judge would permit such discovery. The next stage of the case is expected to involve arguments about what constitutes an emolument.

Nonetheless, for the plaintiffs, the ruling that they have legal standing to challenge the president’s actions is an important first step in their quest to show that Mr. Trump crossed a constitutional line. “We look forward now to proceeding to address the constitutional issues and demonstrate that the emoluments clauses forbid the things of value that are flowing into the president’s pockets from governments foreign and domestic,” said Norman L. Eisen, the chairman of Citizens for Responsibility and Ethics in Washington, who is serving as a co-counsel in the case.

The judge limited the scope of the suit to the Trump International Hotel, down the street from the White House, and businesses related to it that are owned by the Trump Organization. The president’s other business interests — such as the Mar-a-Lago estate in Florida — are not at issue, he found, because they have no clear effect on the plaintiffs.