[mhauru]

Not sure I see what you mean. Here's the infamous I – V – VI – III – IV – I – IV – V progression from Canon in D in just intonation, with square brackets marking tones that make up a chord (invert the chords to your taste): [1/1 5/4 3/2] – [3/2 15/8 9/8] – [5/3 1/1 5/4] – [5/4 3/2 15/8] – [4/3 5/3 1/1] – [1/1 5/4 3/2] – [4/3 5/3 1/1] – [3/2 15/8 9/8]

Of course, you can't do this for every progression you might enjoy playing, but as an example this one works out quite nicely, with no serious harmonic ambiguity or conflict.