Origami-inspired metamorphous structures can adjust their shapes and mechanical behaviors according to operational requirements. However, they are typically composed of nonrigid origami, where required facet deformation complicates actuation and makes them highly material dependent. In this study, we present a type of origami metamorphous structure composed of modular bistable units, each of which is a rigid origami. The elasticity within the origami creases and switching of mountain and valley crease lines enable it to have bistability. The resultant metamorphous structure has multistability, allowing it to switch among multifarious configurations with programmable profiles. This concept was validated by potential energy analysis and experiments. Using this concept, we developed a robotic limb capable of both lifting and gripping through configuration changes. Furthermore, we used the origami units to construct a metamaterial whose properties could change with the variation of configurations. These examples demonstrate the concept's remarkable versatility and potential for many applications.