Here are some movable fingerings for minor 6th chords, shown here as Bbm6. These fingerings are all on groups of four adjacent strings - top four, middle four and bottom four. The next group of shapes are not on groups of four adjacent strings, but all are commonly used shapes which relate to the five basic forms.
Here are some examples demonstrating the use of minor 6th chords. Learn them and then experiment with the ideas presented to come up with your own parts and progressions.