Clever or unusual turns of phrase were regular features of songs from the Tin Pan Alley era. A couple that come to mind:
But Not For Me where “not” becomes “knot” for a surprise ending
Mean To Me where “mean” switches meaning (look, a pun!)
And then there’s the somewhat more recent My Girl Bill by Jim Stafford which is basically a dirty trick.
Well, if we’re bringing out the Simpsons, there’s Ricky Gervais’s song
Lady when you go away, I feel like I could die
Not like dye like your hair is dyed
But die like lady Di
And not like Di like her nam is Di
But die like when she died
Though I guess those are homophones, and not words with multiple meanings.