As diverse robotic hands keep emerging for industrial and household use, designing general grasp synthesis algorithms applicable to multiple grippers remains challenging. To improve the generality and effectiveness of multigripper planar grasping algorithms, we propose a grasping framework featuring gripper-agnostic scene inference and gripper-changeable optimization. In our approach, we introduce an interaction probability map that bridges the scene inference and grasp optimization modules. It efficiently decouples the learning of grasping knowledge and modeling of gripper's kinematics. The inference module adopts a modified directional ensemble method with a generated fingertip dataset to refine scene information. In grasp optimization, we formulate gripper-kinematic constraints for different grippers according to joint types. Extensive evaluations on the Cornell Grasping Dataset (with a success rate of 95.51%) and on multifingered grippers (ten grippers in the real world) demonstrate that our hybrid approach generalizes learnable knowledge across various grippers. This work enables the direct transfer of learned grasping knowledge to new grippers in real-world applications.