This can be acheived on the english concertina,
The secret is to play a melody note and play the chord on the off beat. quite a number of my song accompaniments[ ball of yarn,Tommys lot, greenwood laddie ,just as the tide was flowing etc ]demonstrate this ;its a similiar idea to melody picking on the guitar.
the reason I mention this is that some misinformed person on concertina net, reckoned it was a lost cause on the english concertina.
I have recorded; yesterday ,all my loving, washington post ,dill pickle rag,Rebel Soldier, Bogies bonny belle and many more using melody and chord accompaniment.as have Alistair Anderson[the entertainer]Lea Nicholson [beatles numbers].
its difficult but not that difficult and not a lost cause .Dick Miles