While most soft pneumatic grippers that operate with a single control parameter (such as pressure or airflow) are limited to a single grasping modality, this article introduces a new method for incorporating multiple grasping modalities into vacuum-driven soft grippers. This is achieved by combining stiffness manipulation with a bistable mechanism. The system features a bistable dome structure with a central suction cup and a set of vacuum bending actuators. Designed and optimized using fluid and structure modeling in finite element analysis, it offers three grasping modes: two reflex mechanisms (force- and contact-triggered) and one with active control. All modes rely on the structural buckling of the bistable dome, but differ in how this snap behavior is activated, by force, contact, or active control. Adjusting the airflow tunes the energy barrier of the bistable mechanism, enabling changes in triggering sensitivity and allowing swift transitions between grasping modes. This results in an exceptional versatile gripper, capable of handling a diverse range of objects with varying sizes, shapes, stiffness, and roughness, controlled by a single parameter, airflow, and its interaction with objects.