Conventional rigid-foldable stacked Miura-ori (SMO) mechanical metamaterials could exhibit multistability and reconfigurability corresponding to compressive/extensive deformations only. In this research, the investigation aims to advance the state-of-the-art by extending the multistable reconfigurability to other types of deformations. To tackle this, a novel stacking strategy is proposed, which evolves the traditional SMO cell to a new variant, referred to as a stacked Miura-ori variant (SMOV) cell. The SMOV cell could present eight distinct stable configurations; by switching among them, one can program the underlying kinematical and mechanical properties. Based on the SMOV cell, a three-cell metamaterial beam and a 3 × 3 × 3 metamaterial cube are constructed, and their exceptional multistability and reconfigurability are studied. The beam could exhibit inclined and curved stable configurations that cannot be achieved with the conventional SMO design, and the associated longitudinal sections are tunable. For the cube, the achievable stable configurations are further enriched by the three admissible stacking methods and the unique capability of reconfiguring the inner units without altering the overall shape of the cube. Overall, based on the proposed design innovations, the current level of multistable reconfigurability is significantly expanded, which would provide brand new solutions for developing smart origami metamaterials with environmental and functional adaptability.