This may have already been mentioned, but -
A lot of songs can be sung to the tune of “House of the Rising Sun” including “Amazing Grace” and this Bob Rivers classic: O Little Town of Bethlehem - Bob Rivers (youtube.com)
Any tune with the meter 8 6 8 6 (including hundreds of hymns) can share this melody.
This doesn’t exactly fit the OP, but I think it’s interesting enough to be worth mentioning. Early in the recording sessions for Cream’s “Disraeli Gears” album, they recorded a couple different versions of a song called “Lawdy Mama”. Producer Felix Pappalardi took one of the versions and wrote a whole new set of lyrics, and the song became “Strange Brew”. It’s not the same melody, but it is the exact same backing track on both songs.
