I watched some sort of master class where Alan talks about his harmonic thinking, how he plays and grabs chords. It didn't make sense because he is so idiosyncratic and does not talk the talk of a trained musician. So, we he says he grabs "anything in the chordal family", that translates into a MODAL approach which is key-centered. He says he grabs any notes in the key, basically, regardless of they are stacked thirds/4ths or otherwise.

So, here are the possible voicings to grabber each mode of the Major Scale.

Mode: Voicings
I-(Ionian) 1379, 715, 569, 1473
ii-(Dorian) 2413, 126, 5147, 2415
iii-(Phrygian) 374613, 3695, 34736, 5147
IV-(Lydian) 4736, 4369, 569,4125
V -(Mixolydian) 54673, 4736, 935, 346
vi-(Aeolian) 6514, 64715, 5196, 695
vii (Locrian) 7469, 4735, 2714, 7615