Senator Robert Menendez of New Jersey, a Democrat, was charged in September with accepting bribes, including cash, gold bars and a luxury Mercedes-Benz, in exchange for lucrative political favors and what prosecutors described as efforts to derail criminal investigations.

Federal prosecutors in Manhattan have twice expanded the accusations by filing revised indictments.

In October Mr. Menendez, 70, was additionally charged with conspiring to act as an agent of Egypt while also serving as chairman of the Senate Foreign Relations Committee. And on Tuesday, prosecutors said he had used his power to aid the government of Qatar, a tiny Gulf state and major natural gas exporter that hosted the World Cup in 2022.

Three New Jersey businessmen and Mr. Menendez’s wife, Nadine Menendez, are also charged in the bribery scheme. All have pleaded not guilty, and their trial is scheduled to start in May in Manhattan.

The senator has strenuously denied the charges and has refused widespread calls from fellow Democrats to resign.

Here’s what to know about the complicated schemes that prosecutors believe Mr. Menendez and his co-defendants participated in.

The original indictment revolved largely around Egypt and a halal meat company founded by a longtime friend of Ms. Menendez, Wael Hana, who, like the senator and his wife, is charged with conspiracy to commit bribery.

Mr. Hana, an American citizen born in Egypt, has acknowledged he had no experience in the halal business. Yet within months of operations starting at the New Jersey-based company, IS EG Halal, it became the sole entity authorized to certify that halal products imported to Egypt from anywhere in the world had been prepared according to Islamic law.

The deal resulted in a remarkable change of fortune for Mr. Hana.

In 2018, he lost his home in New Jersey to foreclosure and was on the hook for debts of roughly $890,000. Now he has assets valued at $25 million, according to statements made during a federal court hearing.

Mr. Menendez and his wife are charged with helping Mr. Hana secure the monopoly with Egypt in exchange for bribes that included mortgage payments, gold bars and cash. At the same time, Mr. Menendez, who was then chairman of the Senate Foreign Relations Committee, is accused of steering aid and weapons to Egypt, according to the indictment.

A second businessman charged in the scheme, Fred Daibes, is a developer credited with being at the forefront of the extraordinary residential and commercial growth in Edgewater, N.J., a narrow ribbon of land adjacent to the Hudson River, facing Manhattan.

Mr. Daibes had lost financing for a residential skyscraper he had been planning to build on contaminated land in the borough. He was also battling unrelated federal charges of bank fraud in New Jersey, making it even harder to secure funding.

According to prosecutors, Mr. Menendez introduced him to an investor who was a member of the Qatari royal family and ran an investment company. The company later made a multimillion-dollar investment in the stalled real estate project.

While the deal was being negotiated, Mr. Menendez “made multiple public statements supporting the government of Qatar” and asked Mr. Daibes to share those statements with the investor and an unnamed Qatari government official.

“You might want to send to them. I am just about to release,” Mr. Menendez wrote in a message to Mr. Daibes in 2021, attaching the text of a pending statement. That day, his office issued a news release praising Qatar for agreeing to host Afghans seeking refuge in the United States.

Several days after the investment firm signed a letter of intent related to the Edgewater project in May 2022, Mr. Daibes, Ms. Menendez and Mr. Menendez met for dinner. Hours later, Mr. Menendez performed a Google search for “one kilo gold price,” according to the indictment.

The next month, during searches of the couple’s home in Englewood Cliffs, N.J., and a safe deposit box, investigators seized 13 gold bars, $566,000 in cash and a 2019 Mercedes-Benz. Prosecutors said the car had been given to Ms. Menendez by a third businessman indicted in the bribery scheme to replace a vehicle that police records show she was driving when she struck and killed a pedestrian, Richard Koop, 49, in Bogota, N.J.

Ms. Menendez, who at the time of the December 2018 crash was dating Mr. Menendez, was not tested for drugs or alcohol after the accident and was not accused of wrongdoing.

In addition to Mr. Menendez’s alleged efforts to aid Egypt and Qatar, he is also accused of trying to influence criminal investigations in New Jersey to benefit Mr. Daibes and the third businessman, Jose Uribe.

In 2018, Mr. Daibes was charged by federal prosecutors in New Jersey in a 14-count indictment with plotting to defraud a bank he had founded. Prosecutors claim that Mr. Menendez attempted to install a new U.S. attorney inclined to ease up on the prosecution. The scheme failed, prosecutors said.

Mr. Daibes pleaded guilty in April 2022 to a single count of making false entries in connection with a loan document in an arrangement that did not require prison time. But after he was indicted with Mr. Menendez in September, a judge rejected that plea agreement, scuttling the original deal altogether and complicating the already sprawling web of allegations Mr. Daibes is facing.

Mr. Menendez is also accused of trying to intercede in an insurance-fraud investigation involving associates of Mr. Uribe, a former real estate broker who has also been charged with conspiracy to commit bribery.

In return, Mr. Uribe arranged for Ms. Menendez’s new Mercedes-Benz, prosecutors said.

“You are a miracle worker who makes dreams come true,” Ms. Menendez said in a text message to Mr. Uribe. “I will always remember that.”