Mimi Alford in January 1963, midway through her affair with the president. (Courtesy of Mimi Alford)

Another shocking story from former White House intern Mimi Alford’s memoir about her affair with President Kennedy: He once asked her to do, well, something naughty with his brother Ted.

“Mimi, why don’t you take care of my baby brother,” she recalls him asking when she met the men in a Boston hotel suite in October 1963. “He could stand a little relaxation.”

Alford writes that she flashed back to an earlier episode when JFK urged her to perform a sex act on one of his top aides — but this time, she refused.

We found more sad, sordid stuff in Alford’s memoir, “Once Upon a Secret,” released Wednesday — one of the rare accounts of Kennedy philandering with strong historical corroboration — getting a publicity push on NBC’s “Rock Center” Wednesday night (see below). (**Read earlier: JFK intern shares story of her affair with Kennedy, 2/7/12) Now 69, she divulges that she was mysteriously offered the internship out of the blue — she never applied — a year after she briefly met the president while visiting the White House for a story for her prep-school newspaper. He seduced her over daiquiris her fourth day on the job. She didn’t realize she had a choice, she writes: “I believed if I said no, my dream of a full-time job at the White House would slip away forever.” (Admittedly, “there was a spike in my self-esteem. . . whenever I was with him.”)

President Kennedy addressing the nation during the Cuban Missile Crisis. (AP file photo)

Alford never met Jackie Kennedy, whom she says she greatly admired, and writes that she’s ashamed that “I don’t recall feeling any guilt about my role in her life. In my nineteen-year-old mind, I wasn’t invading the Kennedys’ marriage. I was merely occupying the President’s time when his wife was away.”

They continued seeing each other in the months just after her engagement and just before his death, though their sexual relationship had ceased. It was “proof that I wasn’t just a plaything to him, that he enjoyed my company. . . as a friend,” she writes, but adds: “Perhaps I’m flattering myself.”

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Read earlier: JFK intern Mimi Alford shares story of her affair with Kennedy in new book. Relevant? Historian Robert Dallek says yes, 2/7/12

Read more:

Political sex scandals: Who survives, who burns, 6/5/11

Are affairs still a political dealbreaker?, 11/29/11

JFK Jr. aide recalls secrecy, drama of his final years, 1/21/12

How rich are the Kennedys?, 7/6/11

Joe Kennedy III considers run for Congress, 1/5/12

Rita Jenrette’s new take on an old sex scandal, 11/28/11