They are the models who could bring down a senator.

Sen. Robert Menendez mobilized his staff to secure a visa for a Brazilian actress who posed nude on the cover of Sexy magazine; he stepped up for a sultry Ukrainian student who wanted a plastic-surgery consult; and he directed a staff member to “call Ambassador asap” in order to reverse a visa denial to a 22-year-old Dominican model.

The young women were all paramours of Dr. Salomon Melgen, 60, a married eye doctor and one of Menendez’s biggest donors, prosecutors charge.

The New Jersey Democrat’s efforts on behalf of Melgen’s lovers came to light in a 68-page indictment against the two men unsealed this month.

Menendez is accused of using his power and influence to benefit Melgen in exchange for almost $1 million in gifts and campaign contributions.

If convicted, Menendez faces up to 15 years in prison on each of eight bribery counts alone. Both men have pleaded not guilty.

The senator is also accused of trying to influence a State Department official on Melgen’s behalf in a dispute involving one of the doctor’s business interests in the Dominican Republic.

Prosecutors also say Menendez and his staff tried to help Melgen in a Medicare billing conflict.

Melgen was charged with Medicare fraud last week in a separate 76-count indictment.

But the strangest aspect of the government’s case focuses on Menendez’s Herculean efforts to build Melgen’s harem.

No fewer than six Senate staffers acted with a sense of urgency to get the job done.

The Brazilian

The Brazilian actress — Juliana Lopes Leite, now 34 and a lawyer in Miami — admitted to The Post that she knew Melgen, but declined to comment further.

Menendez, 61, was aware that Lopes Leite was one of Melgen’s girlfriends when he went to bat for her, the indictment charges.

The men have been pals since 1993, when they met at a political fund-raiser shortly after Menendez won his first term in the House. The senator often flew on Melgen’s private plane, sometimes bringing a guest to the doctor’s vacation villa in the posh Dominican Republic resort of Casa de Campo.

When the doctor asked for a ­favor, Menendez jumped.

On July 24, 2008, Menendez ­directed his senior policy adviser, Mark Lopes, to e-mail a high-ranking official at the State ­Department to give “careful consideration” to the visa application of a Brazilian woman — described as an actress, lawyer and model — who wanted to come to the United States on a student visa, legal papers charge.

The woman — identified only as “Girlfriend 1” in the indictment — had applied to study law at the University of Miami.

Lopes wrote that Girlfriend 1, “(no relation to me) has her visa application appointment in Brasilia, Brazil, tomorrow . . . Sen. Menendez would like to advocate unconditionally for Dr. Melgen and encourage careful consideration of [Girlfriend 1]’s visa application.”

The State Department responded within hours, and the woman got her visa the following day.

“The senator very much appreciates your help,” Lopes wrote to the State Department official.

Lopes Leite, who is from Brasilia, received a law degree from the University of Miami in 2010.

By the time the brunette arrived in the United States, she had been a star in Brazil, appearing on the reality show “Big Brother Brasil” and modeling nude in at least two magazines. She left her TV career in 2007 to study law in Brazil, according to an interview in one of the country’s largest daily newspapers.

That was the same year Lopes Leite, then 27, started a romantic relationship with Melgen, then 53, according to court papers.

Lopes Leite met the senator several times in New York, New Jersey, Florida, Spain and at Melgen’s luxury villa in the Dominican Republic, legal papers say.

Lopes Leite said she used the money from her nude photo shoots to partially fund her studies in Miami. Part of her tuition was also paid by Melgen’s nonprofit foundation, according to the indictment.

Tax filings for the foundation, whose self-described purpose is “helping with the educational needs of disadvantaged persons,” show that in 2009, it shelled out $39,961 to pay ­tuition for two students at the University of Miami.

The daughter of a New Jersey woman romantically linked to Menendez also attended the school at that time.

The Ukrainian

Around the same time Melgen became involved with Lopes Leite, he was having a “romantic relationship” with a Ukrainian woman, described by prosecutors as an actress and model living in Spain, and labeled “Girlfriend 3.”

An unnamed Menendez staffer drafted a letter — signed and sent by the senator — to the US consul general in Madrid saying the doctor’s “good friend” needed a visa to “undergo medical evaluation for plastic surgery” and visit him.

The letter contends the woman — then 20 — is a student and “a famous person in Spain” as the face of a TV network and won’t overstay her visa.

“Dr. Melgen is a person of the highest caliber,” Menendez wrote in the February 2007 appeal. “He is a fine citizen and held in high esteem by his peers.”

A week later, the unidentified woman got her visa and traveled to Florida, where she stayed in a Melgen-owned apartment in Palm Beach. She joined Melgen and Menendez for dinner at Azul, a restaurant in Miami’s Mandarin Hotel. Melgen introduced his lover to the senator and told her Menendez helped to get her visa, prosecutors contend.

Melgen has been linked to Svitlana Buchyk, a 28-year-old Ukrainian model who lived in Spain before moving to Florida.

Buchyk was living in a condo rented by Melgen on Singer Island north of Palm Beach in 2009 when she became embroiled in a dispute because her name wasn’t on the lease. Buchyk listed her address as Melgen’s West Palm Beach office, according to a traffic ticket she received that same year for driving with windows that were tinted too dark.

On additional traffic tickets from 2010 and 2011, Buchyk’s address is a North Palm Beach home owned by Melgen.

Buchyk told the Miami Herald in 2013 that she worked for Melgen in the past and that he was “an amazing person.”

“He treated me very well,” she told the paper. “He had money.”

Buchyk now uses the name Lana Moyzuk and lives in Los Angeles. In a bio on her Web site, she says she didn’t come to the United States until 2011.

Buchyk has bounced from apartment to apartment in the past few months.

“We didn’t see her much, but she stuck out,” said Julia Hernandez, a neighbor of the Spanish-style bungalow Buchyk briefly rented in North Hollywood.

Gerald Greenberg, a lawyer for Buchyk, said she and Melgen were friends. He declined to comment further.

The Dominican

Menendez and his staffers went to the greatest lengths to obtain visas for a 22-year-old Dominican woman — identified by prosecutors as “Girlfriend 2” — and her 18-year-old sister, who wanted to visit Melgen around Christmas in 2008.

The doctor wrote to the US Embassy in Santo Domingo on Oct. 13, 2008, assuring officials he would cover expenses for the sisters and that they would return home. That same day, he asked Menendez to follow up with the embassy in ­order to “move the letter along.”

Menendez passed on the request to Lopes, his senior foreign-policy adviser whose actual duties included representing Menendez on the Senate Foreign Relations Committee. The staffers drafted a letter from Menendez to the consul general and asked that the sisters’ applications be given “all due consideration.”

The senator told Lopes to not only send the letter but to call “if necessary.” But after their interview, an embassy employee denied the visas for the sisters, saying that neither was working and that they had “no solvency of their own.”

When Menendez learned of the denial, he told Lopes, “I would like to call [the] ambassador tomorrow and get a reconsideration or possibly our contact at State.”

An unnamed high-ranking State Department official wrote to Menendez that he agreed with the rejection, saying the sisters had not been convincing about their eventual return to their home country. But a few weeks later, the State Department decided to re-interview the women, and they were granted visas.

When the approval finally came, Lopes wrote in an e-mail to a colleague that it was “ONLY DUE to the fact that RM intervened.”

Lopes refused to comment.

Additional reporting by Jose ­Ernesto Devarez , Linda Massarella and Julie Kay