A container forming assembly and method includes receiving a parison within a cavity of a mold, enclosing the parison within the mold having a wall with a recess, inflating the parison in the mold to form a blow molded container where the blow molded container has a sidewall, a movable region formed at the recess, and a hinge circumscribing an interface between the sidewall and the movable region, and moving or repositioning the movable region toward an interior of the blow molded container about the hinge before filling. The movable region can form a deep-set grip. Further, multiple movable regions can be provided, each of which may form respective deep-set grips. The container shape can be symmetrical or asymmetrical.