Many years ago I picked up a book called called 'Folk Tunes to Accompany: Modes and Minors' (1971) by Robert Noble. I've not found anything since that addresses so explicitly the issue of harmonising modal tunes.

His basic approach is to build triads, but only on the actual notes used in the mode. For example, if you have a 'pre-Aeolian' tune in A with no 6th note, you wouldn't use any chords containing F.

On the concertina I'm learning (a Crane Duet), it is certainly easier to use broken chords based on the 1st and 5th notes which I presume are equivalent to Power Chords on a guitar, than to bring in the 3rds, but that's quite possible too. On an Anglo Concertina (or Melodeon), however, it's very easy to play in thirds, but the results can be unusual by the standards of modern harmony. Dan Worrall's book on William Kimber covers this in detail.