I have personally had songs jump onto tunes, and I am sure (as BB sometimes points out) that I have had songs that were quite similar to others, and even when it is pointed out I can not hear the similarity.

I had a song about cows jump onto Richard Baker and several jumped onto Livet in Fineskogin, which probably is my default tune, and Rhyme of the Ancient Mariner (oops can't say I wrote that one) jump onto Star of the COunty Down, which I never ever would intentionally use because it has its own words. One jumped onto Dainty Davy. So they do jump, although perhaps I am the only person in the entire world this happens to. And one by Kipling jumped onto Auld Lang Syne. Another by Kipling jumped onto one of the Twa Sisters tunes. mg