High-DOF dexterous hands require compact actuation, rich sensing, and reliable thermal behavior, but conventional designs often occupy valuable in-hand space, increase end-effector mass, and suffer from heat accumulation near the hand. Remote tendon-driven actuation offers an alternative by relocating motors to the robot base or an external motor hub, thereby freeing the fingers and palm for additional degrees of freedom, sensing modules, and maintainable mechanical structures. This paper presents MM-Hand, a 21-DOF Multimodal Modular dexterous hand based on remote tendon-driven actuation. The hand integrates spring-return tendon-driven fingers, modular 3D-printed finger and palm structures, quick tendon connectors for maintenance, and a multimodal sensing system including joint angle sensors, tactile sensors, motor-side feedback, and in-palm stereo vision. We further analyze tendon-sheath length variation and friction loss to guide the design of the routing, motor hub, and closed-loop joint control. Experiments validate the transmission, output force, sensing, and control capability of the system. The fingertip force reaches 25N under a 1m remote sheath transmission, demonstrating practical load capacity despite long-distance tendon routing. Closed-loop joint-level experiments further evaluate command tracking with a static arm and during arm motion. These results show that MM-Hand provides a lightweight, sensor-rich, and maintainable hardware platform for dexterous manipulation research. To support the community, all hardware designs and software frameworks are made fully open-source at https://mmlab.hk/research/MM-Hand.