Theory

Imaj9 = IIIm7, I6 = VIm7, Imaj13 = IIIm11
ex:
Cmaj9 = Em7; C6 = Am7, Cmaj13 (no root or 5th) = Em11 (no 3rd)

I9 = IIIm7b5, I7add13 = VImaddb9, I13 (no root or 5th) = IIIm7b5(add 11, no 3rd)
ex:
C9 = Em7b5, C7add13 = Amaddb9, C13 (no root or 5th) = Em7b5(add 11, no 3rd)

Im9 = bIIImaj7, Im6 = VIm7b5, Im69 (no root or 5th) = bVIImaj7(add11, no 5th)
ex:
Cm9 = Ebmaj7, Cm6 = Am7b5, Cm69 (no root or 5th) = Bbmaj7(add11, no 5th)