In situ tuning of elastic stiffness enriches the range of functionalities of mechanical metamaterials for next-generation multifunctional devices. While stiffness tunability has been demonstrated under compression and tension, tuning flexural stiffness in multistable materials is now addressed in this work. Researchers leverage a multistable topological transformation induced by internal contact to activate zero-energy modes that yield both stiff and soft flexural modes. This remarkable tunability of flexural stiffness endows the architecture with a reversible rigid-flexible switch, which could support diverse applications from soft robotics to medical devices.