Not necessarily regarding sequels, but I love it when the sound-alike follow-up to a big hit is written by different people from the first one (e.g., Mann & Weil wrote "You've Lost That Lovin' Feeling". and Goffin & King wrote "For Once In My Life"). It was a Brill Building competition thing.

Ernie K-Doe's "Mother In Law", followed by Benny Spellman's "Lipstick Traces". Check it out. Of course, this doesn't count Answer Records (e.g., "The Girl From Wolverton Mountain")
or parodies (anything by Ben Colder). I am writing a book about this and other related 1960s music topics, called "Strictly…