You can play X7b9 or X7b9b13 chords.
Let's take D7b9, for example. You take the D bass from the major third bass row and play Eb dim chord from the diminished row. As a result you get D bass + Eb-Gb-C chord. In a similar way, you play D7b9b13 when you press the same D bass + Eb minor from the minor chords row + Eb dim and you get D + Eb-Gb-Bb-C.
A good book, containing a table with more than 40 chord combinations + theory and exercises is: "Accordion Jazz Chords, Free improvising on the stradella bass accordion" by Norbert Seidel (ISBN 3-925572-09-0). I think it can give a lot of inspiration for unleashing the freedom with the left hand.