Some folks say that "Roll On, Columbia" was written to the tune of "Goodnight, Irene." Actually, the tunes seem slightly different to me, but the two songs could definitely be sung together.

"Do, Lord," has virtually the same tune as "This Little Light Of Mine." Even when "This Little Light" is sung to a slight tune variation, they can still be sung as partner songs.

Also, several rounds can be superimposed on each other--e.g., Three Blind Mice, Frere Jacques, and Row, Row, Row Your Boat.