The kind of thing I mean is, for example, if the boukouki is tuned ADAD, you just leave the A strings open, and fret the other two in unison moving up and down the fretboard to where it sounds right, strumming the whole set of strings all the time.

Or just play fretting one of the D strings it somewhere high up on the neck, and start picking out bits of the tune on various strings, so that at all time two or three strings are being played open.

Everything you do could be given a name as a chord by someone who was into that, but you really aren't thinking in terms of chord sequences as such.