It's nearly always possible to get the intonation "right" on a wrap around bridge assuming that it has been set in the right place with the right compensation or offset. It will also always be "wrong" Its the nature of the beast. It requires an acceptance of a basic premise. Our modern western tuning temprement is 12 note ET which is a compromise in itself. No guitar will ever have perfect intonation right the way across the neck, in fact you don't want it to. What your after is the best all round compromise so that the ear will tell you that everything is OK. As has been suggested the most common way to achieve this is to set the fundamental harmonic at the 12 fret which is the octave to match the fretted note at the same place. This will normally give you the best all round intonation for 12 note ET. You then need to set the relief and action to get the right intonation for the string gauge.
If you can imagine that the string is stretched as you fret it the tuning is raised relative to the fret position or sounding string length. The amount the pitch is raised will become greater as you go up the neck because you have to push the string further and there is less string to be stretched.. Clearly then the note at say the 5th fret is going to be raised in pitch less than say the 17th fret an octave higher. Again a compromise that the fret spacings accommodate to get you in the right ball park. All ET tunings are a series of compromises. In the days before 12 note ET was adopted lute and viol players would use this to their advantage as they moved the gut frets to get perfect fifths and thirds by setting the frets in a very similar way to the modern guitar. They also adjusted for the varying quality of gut strings by slanting the frets. Other instruments like the spinet or harpsichord were tuned in other temperaments to give perfect fifths and as a result other intervals would sound terrible (at least to our ears). Even the same intervals in different keys would be out. Composition at the time took all this into account.
So, if you have the intonation at the 12 fret right with the harmonic and the fretted note, raising the action will sharpen notes above the 12fret more than below it and lowering the action will bring them closer together. String gauge will also play a part in this. Also important is clean new strings old strings lose their ability to intonate because the material stretches and loses its uniform stiffness and mass per unit length. So when setting intonation always use good branded and new strings. If you cannot get good intonation by adjusting the action and the neck relief then The bridge is in the wrong place or the action is way to high.
If was impossible to set the correct intonation on a wrap around bridge then it would be impossible to get an
acoustic guitar with a single saddle to play in tune. Clearly that isn't the case.
I've found over the years that a lot of players that come to me to have the intonation looked at are often expecting too much from the modern 12 note ET system itself. They are listening for perfect fifths, thirds and octaves and in 12ET it just aint possible although we can get very very close.
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