When my friends and I sang it in New York City in the late 1950s, early 1960s, we incremented the story in each chorus, something like,

Jack and Jill went up the hill/To fetch a pail of water/Jack fell down and broke his crown/And threw it out the window, the window/The FIRST story window/Jack fell down and broke his crown/And threw it out the window,

then Mary threw her little lamb out the SECOND story window, Jack Horner threw his plum out the THIRD story window, and so on.