All Of Me follows an A B A C form. I use the standard key of C major for this reharm. The bulk of the tune uses a cascading sequence of V - I changes pivoting around Eb - G - B tonal centers. It can get a little tricky to keep track of where you are. The end of the B section moves into the E - C  tonal centers, which suggest the third party of Ab, and then a half-step II - V moves us back down to F-7 to start the cycle again. The second ending pivots into G major until the Ebmaj7#5, then begins to cycle again, even as the Eb resolution is sounded. 

I had to tweak the melody at the end of the first A section into the B section as follows: In the last measure of the A section, the F is held for a half-note, then the E which would normally come in the next measure sounds on beat three for a half-note. The B section begins with the D# as a half-note, and then the D natural is played for a full half-note starting on beat three. This was the only adjustment needed.

There is an intro and a coda for this one. The coda drops to E and then used that as a pivot into the E - C - Ab tonal centers, which allow the ending in C. I also use the stock ending, but end on a Cmaj7#5 to bring out the G# as the continuation of the F - F# - G part of the line. Here are my changes: