Then of course there is I Love Paris by the great Cole Porter. The chorus has 16 bars in the minor key followed by virtually the same melody in the major (achieving a sudden brightness from Bar 17). The first sixteen bars could be in C minor, the next sixteen in C major.
I may be wrong, but I think the proportion of classic songs using the harmonic key-changing trick is probably fewer than 10%. But they form an interesting group – offering so much more of a challenge to the musician and improviser than the hundreds of tunes with orthodox harmonic patterns.