These were pretty common in early pop music, less so now. Songs that were responses to earlier songs.
The classic example, from what I have read, is Hank Ballard and The Midnighter's 'Work With Me Annie'
And as Wikipedia says:
"Work with Me, Annie" is a 12-bar blues song with words and music by Hank Ballard. It was recorded by Hank Ballard & the Midnighters (formerly The Royals) in Cincinnati on the Federal Records label on January 14, 1954, and released the following month. The Federal Communications Commission (FCC) immediately opposed it due to its overtly sexual lyrics, lyrics that had crossed over and were now being listened to by a white teenage audience. Because the record was in such demand and received so much publicity, attempts to restrict it failed and the record shot to number one on the R&B charts and remained there for seven weeks.
This was the first of the "Annie" records and sold a million copies; so did the answer songs "Annie Had a Baby" and "Annie's Aunt Fannie." They all were banned for radio play by the FCC. The success of these recordings spurred the practice of recording double entendre records and answer songs. Another answer, "The Wallflower", by Etta James, popularly known as "Roll with Me, Henry", was reworded by Georgia Gibbs as "Dance with Me, Henry" for Top 40 consumption. It had the same melody as "Work with Me, Annie". The melody was recycled again by the Midnighters for the song "Henry's Got Flat Feet (Can't Dance No More)".
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