Feeding the drift, I know, but Bill Monroe used a harmony tuning on mandolin for 'Get Up John'. Major thirds, I think, but not on all the strings.
Back to twelve strings; I have one and a half 12 strings. The one is a very early Seagull; I use D'Addario light gauge strings on this, and tune it to concert, and occasionally DADGAD. This gives a good action and excellent intonation. I tried tuning it down, but the action felt 'floppy'. The half is one half of a 1975 Rob Armstrong 12/6 doubleneck; due to the age and value of the instrument, I tune this one down two semitones, and use Elixir light/medium hybrid strings (saves having to change them so often, always a pain on 18-string guitars!). This has had an unexpected benefit over Christmas. Mant of the carols I've been playing are sung in F; not normally the nicest key for guitar, but the 12 makes it easy; just play the simple key of G shapes. I tune the six string neck to concert, or dropped D.
Tim