I really didn’t know these existed until I recently listened closely enough while shuffling among artists on my iPod and made the mental links.
Judy’s Turn to Cry is a sequel to It’s My Party (and I’ll Cry if I Want To) --both by Leslie Gore
Bye Bye Johnnie is a sequel to Johnny B. Goode – both by Chuck Berry
Can you name some others?
Jimmy Dean: Big John’s Cajun Queen
Tommy and Gina, the central characters of Bon Jovi’s Livin’ on a Prayer, were referenced briefly in their later song It’s My Life.
Major Tom
Space oddity - David Bowie
Ashes To Ashes - David Bowie
Major Tom - Peter Schilling
Mrs. Major Tom - K.I.A.
Hallo, Spaceboy (Remix) - Pet Shop Boys
Jeez, you folks are up late.
It’s ten-thirty here.
There was a sequel to Harry Chapin’s Taxi. It was called Sequel.
You’re good, Johnny. My dad was in the music business and I absorbed a lot just from being around him. And I knew that Harry Chapin did in fact do a sequel to Taxi, but for the life of me I could not remember the title.
I am suitably impressed and I thank you for getting that “worm” outta my mind.
Hank Ballard and the Midnighters and Etta James (W/ Harvey Fuqua) had a back and forth thing going in the 50’s.
The Midnighters recorded “Work with me Annie” and Etta answered with “Dance with me Henry (The Wallflower)” the Midnighters then recorded “Henry’s Got Flat Feet.” They also recorded “Annie had a Baby” not clearly a response, but definitely a sequel.
There was a sequel to “The Devil Went Down To Georgia” called “The Devil Comes Back To Georgia.” It featured Johnny Cash and Travis Tritt on vocals and Charlie Daniels on fiddle.
Daniels also recorded a loose sequel to “Uneasy Rider” called “Uneasy Rider '88.” In it, the protagonist and friend make an ill-fated visit to a gay bar.
R. Kelly’s horrid Trapped in the Closet has 12 chapters. 
Thanks so much for reminding me of Peter Schilling. Just been watching some of his vids on youtube
Marty Robbins followed his hit El Paso, a first person ballad about a cowboy with a doomed love “for the Mexican maiden” in “Rose’s Cantina”, with a sequel, El Paso City, in which the narrator is in a plane contemplating whether he is the reincarnation of the man from El Paso.
Snoopy’s Christmas as a sequel to Snoopy vs. the Red Baron.
Buddy Holly - Peggy Sue / Peggy Sue Got Married
There was also Little Bitty Big John.
Buddy Holly did Peggy Sue Got Married as a sequel to Peggy Sue.
e.t.a. - what Peter Morris said.
Similarly:
LaVern Baker - Jim Dandy/Jim Dandy Got Married
The Unforgiven and The Unforgiven II by Metallica
Danny Aiello, the father in Madonna’s “Papa Don’t Preach” video, recorded a reply song called “Papa Wants the Best For You.”
“Leslie Anne Levine” is a sequel to “We Both Go Down Together” (both by the Decemberists), according to the band. “Leslie Anne Levine” was written (or at least recorded) first, though.