As a belated birthday present, the Doctor takes Peri to 1971 Las Vegas to see the King of Rock 'n Roll, Elvis Presley, in concert. But the King seems uncharacteristically late to hit the stage, so the Doctor leaves Peri sipping cocktails and investigates, making his way up to Elvis's penthouse suite at the Hilton. There he's gassed and hauled aboard a spaceship hovering in mid-air over the Strip, to find Elvis knocked out and hooked up to a DNA splicer. The ship's crewed by three one-eyed Mongarians (Malarch, Heckran and Goorg) who think the Doctor's a competitor trying to steal their plan. They're 24th century peddlers, hawking knock-off Elvis merchandise at conventions, who are fed up with their Slarvian competitors outselling them with quality reproduction autographs. So they've gone one better - they've stolen a time machine and have been going up and down Elvis's timeline, abducting him and harvesting DNA samples to turn into clones of the man himself that they can sell.
Before they can throw him out an airlock, the Doctor steals a gun from one of them and threatens a rare 1977 ceramic bust of Elvis from their collection. He forces them to listen to a recording of "Love Me Tender", arguing that no clone could ever equal the talent of the real thing. They may look like him, they may sound like him - but they'll never BE him. His emotional appeal works, and the Doctor is returned with Elvis to the suite. He wakes the King up and gently prods him to the show, then returns to Peri's side to watch (as are the sunglasses-wearing Mongarians a few tables away). Before he starts singing, though, Elvis has a special message for the man he suspects is in the audience, the man he suspects saved his life: "Thank you very much."
And as he presents Peri with the autograph Elvis signed for her birthday, the Doctor whispers: "No, Mr Presley, thank YOU very much."
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