Not traditional folk, but folk-y: You could try the original 1582 version of Gaudete from Piae Cantiones, which I remember singing as a four-part, and Steeleye re-worked as (I think) a three-part - their verse melody was quite different, though nicer, but the refrain was the same. Certainly my handwritten score, done by a friend, had at least four lines. We used to busk it in the pubs around Christmas. It's certainly lively and pleasing.

Link here which may be of some interest: Andrew Greenhill