The DC-area group Clam Chowder does a wonderful version of the medieval Deo Gratias Anglia to the tune of the Banana Boat Song. They sing one verse straight first --
Our King went forth to Normandy
With faith and might of chivalrie
Therefore England doth call and crie
Deo Gratias Anglia
before the tenor breaks out into Belafonte's
Deo!
De-e-e-oh!
Deo gratias Anglia
The calypso rhythms start, and it all goes downhill from there.
In Sacred Harp music, there's the concept of Common Meter -- 4/4 time with a particular line length. Anything in CM, such as Amazing Grace, can be sung to the tune of anything else in CM, such as O Little Town of Bethlehem, or House of the Rising Sun, or Yellow Rose, or many more.
LynnT