The 160-page complaint alleges that Mr. Trump and his family received secret payments from three business entities in exchange for promoting them as legitimate opportunities, when in reality they were get-rich-quick schemes that harmed investors, many of whom were unsophisticated and struggling financially.

Those business entities were ACN, a telecommunications marketing company that paid Mr. Trump millions of dollars to endorse its products; the Trump Network, a vitamin marketing enterprise; and the Trump Institute, which the suit said offered “extravagantly priced multiday training seminars” on Mr. Trump’s real estate “secrets.”

The four plaintiffs, who were identified only with pseudonyms like Jane Doe, depict the Trump Organization as a racketeering enterprise that defrauded thousands of people for years as the president turned from construction to licensing his name for profit. The suit also names Donald Trump Jr., Ivanka Trump and Eric Trump as defendants.