At the annual Springfield Pride Awards hosted by Kent Brockman and Britney Spears, awards are given to prominent Springfield citizens for their achievements. They present the award for the oldest man in Springfield to Cornelius Chapman, who is 108 years old. Chapman comes up to accept his award, but when Spears gives him a congratulatory kiss on the cheek, he dies of a heart attack. The award is therefore given to the now oldest Springfieldian in the crowd, Mr. Burns. After Burns wins, he realizes he is not a young man anymore, so he and his assistant Smithers go to the Mayo Clinic in Minnesota for a check-up. Burns decides to give the Simpson family an opportunity to house sit his private mansion while he is being tested for various diseases.
After enjoying life as a billionaire for a few days, Homer decides to throw a party before Burns returns. He heads to Moe's Tavern to buy some beer and invite his friends to the party. However, Moe informs Homer that he can not sell him alcohol on account of it being Sunday before 2:00 PM. After Homer is told the only way he could buy alcohol would be to sail out to international waters where there are no laws, he and his friends (including his son Bart) set sail in Burns' private yacht to throw the party there. Back at the Mayo Clinic, Burns discovers that he not only has all previously discovered diseases, but numerous new diseases the doctors have just discovered in him. However, the sheer number of diseases prevents any one disease from actually doing harm to him. This leads Burns to (incorrectly) conclude that he is indestructible, even though the doctors protest that even a slight breeze could disrupt the balance in his body.
Meanwhile, the party continues and the party goers force Burns' monkeys into having a knife fight. The yacht is eventually boarded by Chinese pirates who take the ship hostage. The pirates rob everyone on board and tie them up in a net which they then toss overboard. But to the luck of Homer and some of the other guests who happen to be above ocean surface level, it floats and they avoid drowning. Eventually Homer and Bart make it back to the mansion where the family returns the house to Burns after Marge and Lisa have scrubbed all the rooms clean. Back at the Simpsons home, everyone is glad to live a normal life again—with the exception of Homer, who is upset that he does not live the lifestyle of rich people. The episode ends with Homer wailing about how rich all the persons in the closing credits are (except Richard K. Chung, whom he dismisses as poor) and threatening to report them to the Internal Revenue Service and telling the Gracie Films woman not to shush him.