This work addresses sequentially grasping multiple objects with a single dexterous hand without releasing those already held. Most dexterous grasping methods commit all of the hand's degrees of freedom to a single object, underutilizing its dexterity and leaving no redundancy for subsequent grasps. The proposed solution, MoDex, is a diffusion policy that predicts the next gripper pose directly from observations, conditioned on an opposition space and point cloud. The opposition space condition specifies which fingers participate in the current grasp, enabling the gripper to use only a subset of its available degrees of freedom while reserving the remaining degrees of freedom for subsequent grasps. To facilitate sim-to-real transfer, MoDex is trained in two stages: first through imitation learning on expert demonstrations, and subsequently through reinforcement learning fine-tuning, which consistently improves success rates over the pre-trained policy. We evaluate MoDex in simulation on a MuJoCo-based Franka Emika Panda robot equipped with an Allegro Hand and on the corresponding real-world hardware platform. Across both simulation and real-world experiments, MoDex achieves higher success rates than the evaluated learning-based baselines, improving performance by 2.92-17.92% and 6.67-17.78%, respectively. Project page: https://modex2026.github.io/.