I would disagree with alanww about the English Concertina. It is very easy to play chords - it's trying to play multiple melodies which is difficult. This is because alternate notes are on different ends of the instrument and so the parts tend to cross hands all the while. It's very suitable for playing a melody with fill-in chords and easy to accompany songs with.

The Duet Concertina was introduced partly to overcome the above-mentioned limitations of the English concertina. Beware though, Duets come in at least 4 different key layouts - McCann, Jeffries and Crane (or Triumph), and the later Hayden system.