Underactuated graspers are known for their self-adaptability. The configuration in which it obtains a stable grasp relies on static force equilibrium. Any external or inertial forces acting on the seized object disturb this static equilibrium and tend to change the configuration of the grasper. Self-adaptability therefore challenges the robustness against external perturbations. This paper introduces the concept design of an underactuated grasper with the ability to adjust its level of self-adaptability by changing the rotational stiffness of its differential mechanism. To avoid an additional actuator for this adjustment, a bi-stable mechanism was implemented which changes the actuation type of the differential from a point force in the compliant state to an antagonistic couple in the stiff state once the actuator force overcomes a threshold value. Experimental validation of the concept design shows that the lateral compliance of the grasper in the stiff state reduced by a factor 7 compared to the compliant state. Also, the lateral pullout force in the stiff state increased by a factor 1.9. Thus a grasper was designed which uses the benefits of self-adaptability to grasp an object and increases its robustness once a stable grasp is obtained.