The detuned string in between likewise has a perfect octave relationship to strings that are two removed.
The E, D and B strings are turned such that they yield clean octaves (and other equal-temperament intervals).
Then so are the A, G and E.
But these two groups are slightly detuned, so that the fifths are clean from the E to A string, D to G, and B to E.
Have you actually tried this? What songs work? To me this sounds totally impractical and useless, like it’s a logical technicality for the purposes of this discussion and not something a real musician would ever do. You’re making tuning a pain, breaking the E-E octaves (all barre chords), breaking octaves with 2 strings between, breaking the next-string octaves, breaking a lot of scales and jazz chords, and to top it off it would still only work for certain keys and not others. I’ll pass.
1. Yes; I've been tuning along those lines for nearly four decades. What songs work: anything with power chords that benefit from sounding sharp, free of flutter.
2. The error between the equal temperament perfect fifth and the pure one (3/2) is just less than 2 cents. So the difference I'm talking about is at the same level of accuracy as that of pretty excellent guitar intonation. The corrections are not simply for equal temperament; they are not separable from the condition of the instrument and its intonation. The given instrument is what it is, and to get those 1-5-8 power chords to sound clean you do whatever you have to.