This is one I've seen Bireli use.
I don't quite understand how he uses over changes but the gist of the idea is that 4th structures are found all over the place in chords and he simply shifts a few frets to outline different chord tones. He will also push the time outside as well, or go to half-time phrasing. If I remember correctly, there were instances where he'd use his pinky somewhere in there as well;
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On a major chord, you can use this "grip" with the root, 9th, 5th, and 6th voiced in the melody (highest) note.
On a minor chord, you can use it with the root, 3rd, 11th, 5th, 7th in the melody.
Dominant chords... I'll leave this one up to you since there are so many possibilties for extensions (including the 7sus sound as well). Experiment to see how "out" sounding you can get with it - IE try and get at least one altered extension in each grip to emphasize the dominant resolution.