Interesting that this intersects with something I've been experimenting with lately. A friend of mine came up with a way of doing 41-tone equal temperament on a modified guitar [1]. One of the tricks is that since 41-TET would require the frets to be so tightly packed that the guitar would be difficult to play, you simply omit every other fret and tune the guitar so that each string has the notes its neighbors on either side lack.
It's a little strange not having all the notes on all the strings, but it actually works out surprisingly well. Chord intonation is a bit nicer than 12-TET, and you get pretty good approximations of the 7-limit just intonation intervals as well.
There's a similar trick with a normally fretted guitar: tune the strings in alternating major and minor thirds (something like ACEGBD) and lower every other string by 15 cents. Then any three adjacent strings will be a just intonation major or minor triad, you can mini-barre them on any fret to get more triads, and there are just intonation scales in every key.
I haven't heard of that one, but I have heard of simpler tricks like re-tuning one string so the third of certain barre chords comes out right. There's always a bit of a trade-off; some intervals get better and others get worse so in effect you're optimizing the instrument for a particular playing style or key or song.
If you're willing to modify the guitar to put frets in different places, it allows for a lot of options you wouldn't have otherwise. (This is especially true if you're willing to use partial frets.)
Kite tuning is the best scheme I've encountered for having closer-to-just intervals than 12-TET and yet you can play in any key. If you want perfect intervals, plain just intonation is better but then you're locked into a particular key and scale.
The design space of guitar fingerboards is surprisingly huge and open-ended when you stray even a little from the twelfth root of two as the fundamental unit of musical interval width.
It's a little strange not having all the notes on all the strings, but it actually works out surprisingly well. Chord intonation is a bit nicer than 12-TET, and you get pretty good approximations of the 7-limit just intonation intervals as well.
[1] https://en.xen.wiki/w/The_Kite_Guitar (The 7-string Ibanez is mine.)