It is more limiting if you only use two fingers per side. The simplest chord is a triad (like G, B, D in ascending order) which you'd play as a block of three buttons on the same side. But there's always a way of moving one or more of those notes to a different octave, so every chord can be played in some form using no more than two keys on each side. You'll inevitably develop a unique style of accompaniment. Even one or two notes at a time can produce perfectly satisfying harmonies; in fact you'll avoid the tendency to swamp the song with over-thick chords.

I look forward to you becoming the Django Reinhardt of the English concertina :-)

Anahata