We present the Magnetic Origami Reprogramming and Folding System (MORF), a magnetically reprogrammable system capable of precise shape control, repeated transformations, and adaptive functionality for robotic applications. Unlike current self-folding systems, which often lack reprogrammability or lose rigidity after folding, MORF generates stiff structures over multiple folding cycles without degradation in performance. The ability to reconfigure and maintain structural stability is crucial for tasks such as reconfigurable tooling. The system utilizes a thermoplastic layer sandwiched within a thin magnetically responsive laminate sheet, enabling structures to self-fold in response to a combination of external magnetic field and heating. We demonstrate that the resulting folded structures can bear loads over 40 times their own weight and can undergo up to 50 cycles of repeated transformations without losing structural integrity. We showcase these strengths in a reconfigurable tool for unscrewing and screwing bolts and screws of various sizes, allowing the tool to adapt its shape to different bolt sizes while withstanding the mechanical stresses involved. This capability highlights the system’s potential for task-varying, load-bearing applications in robotics, where both versatility and durability are essential.