The common hexagon twist options when folding grid-based origami tessellations are closed and open hexagon twists with mountain folds of pleats coming directly to the center or one grid spacing away from the center, respectively. Allowing each pleat in a hexagon twist to be positioned independently in an open or closed state provides 12 additional collapse possibilities without adding new creases to the paper beyond the central hexagon of the open hexagon twist. These hybrid options between the closed and open hexagon twists can be folded directly on a grid without marking additional reference creases and they also represent an opportunity for highly reconfigurable mechanisms due to the limited number of folds that give rise to all 14 total options. This paper will also demonstrate a method for direct substitution of hybrid hexagon twists into broader tessellation patterns and showcase the tessellation design space opened up by these new twist options.