For robot arms to perform everyday tasks in unstructured environments, these robots must be able to manipulate a diverse range of objects. Today's robots often grasp objects with either soft grippers or rigid end-effectors. However, purely rigid or purely soft grippers have fundamental limitations: soft grippers struggle with irregular, heavy objects, while rigid grippers often cannot grasp small, numerous items. In this paper we therefore introduce RISOs, a mechanics and controls approach for unifying traditional RIgid end-effectors with a novel class of SOft adhesives. When grasping an object, RISOs can use either the rigid end-effector (pinching the item between non-deformable fingers) and/or the soft materials (attaching and releasing items with switchable adhesives). This enhances manipulation capabilities by combining and decoupling rigid and soft mechanisms. With RISOs robots can perform grasps along a spectrum from fully rigid, to fully soft, to rigid-soft, enabling real time object manipulation across a 1 million times range in weight (from 2 mg to 2 kg). To develop RISOs we first model and characterize the soft switchable adhesives. We then mount sheets of these soft adhesives on the surfaces of rigid end-effectors, and develop control strategies that make it easier for robot arms and human operators to utilize RISOs. The resulting RISO grippers were able to pick-up, carry, and release a larger set of objects than existing grippers, and participants also preferred using RISO. Overall, our experimental and user study results suggest that RISOs provide an exceptional gripper range in both capacity and object diversity. See videos of our user studies here: https://youtu.be/du085R0gPFI