It you create a new version that adds original melody elements anywhere in the song you can register it as a new work.
For example: You have done some melodic modifications to “Jingle Bells” and given it a Latin treatment that changes the song, you can call it “Jingle Bells Samba.” It is based on the original work (derivative), but by adding new elements becomes a new composition.
Think “Hush Little Baby” (the Mockingbird song). The original, traditional folk song is PD. But “Mockingbird” as created by James Taylor & Carly Simon is a protected copyright, despite its PD source.