The success of hybrid suction + parallel-jaw grippers in the Amazon Robotics/Picking Challenge have demonstrated the effectiveness of multimodal grasping approaches. However, existing multimodal grippers combine grasping modes in isolation and do not incorporate the benefits of compliance found in soft robotic manipulators. In this paper, we present a gripper that integrates three modes of grasping: suction, parallel jaw, and soft fingers. Using complaint handed shearing auxetics actuators as the foundation, this gripper is able to multiplex manipulation by creating unique grasping primitives through permutations of these grasping techniques. This gripper is able to grasp 88% of tested objects, 14% of which could only be grasped using a combination of grasping modes. The gripper is also able to perform in-hand object re-orientation of flat objects without the need for pre-grasp manipulation.