Try listening to Charlie Parker. Most of his "compositions" began as improvised solos to standard tunes. The best known example would be "How High the Moon" and "Ornithology."

Although the Yardbird did not generally commission lyrics for his compositions, words have been set to them by others, such as Jon Hendrix or Dave Lambert.

The fact is that the key to this is in the chords. Virtually any blues has hundreds of other songs that could be fit to the same accompaniment. The same can be said for most popular music. Try the "I've Got Rhythm" or the "Blue Moon" chord progressions and any number of songs should come to mind.

The trick is not to find songs that can be sung together, that is easy to do. The trick is to find songs that are worth singing together. Songs are only worth singing together if the melodies yield a pleasing counterpoint or if the combination of the lyrics produces a worthwhile insight of some sort. Its best when both things happen.