All The Things You Are* follows an A A B A form, where each A section is a variation. In the original, the first A section uses the keys of Ab and C, the second A section moves the melody into the keys of Eb and G, and in the final A section, the overall key of Ab prevails, with an added four bars, making it a twelve-bar section. I use the melody from the original key.  

I only had to tweak the melody at the end of the last A section as follows: in measure 9, the F which normally occurs on (or around) beat two is changed into a Gb. This was the only adjustment needed.

The tritonic groupings are as follows: in the first A section, the keys of B, G, and Eb precede the keys of F, Db and A. In the second A section, the keys of F#, Db and Bb precede the keys of C, Ab, and E. (This maintains the same down-a-fifth relationship as the original harmony.) The B section begins with the same grouping of C, Ab and E, and is followed by the keys of A, F and Db. The last A section mimics the first, adding the keys of D, Bb and Gb for the extra four bars. All twelve keys are represented.  Here are my changes: