Robotic manipulation dexterity is often pursued by building increasingly complex high-DoF multifingered hands. While many robotic hands are designed to replicate human morphology, the functional role of human hands suggests a different perspective: much of their complexity may exist to enable tool use and tool making. This observation motivates Any-ttach, a tool-centric manipulation framework that treats quick end-effector swapping as a mechanism for dexterity with simplicity. Any-ttach combines a low-cost automatic swapping mechanism for an open-close robot interface, a handheld device for collecting human demonstrations, and a task planning framework that composes learned, parameterized, and planned tool-use skills. The system supports diverse tools and end-effector modules, including daily tools, articulated tools such as scissors, Fin Ray fingers, and a low-cost anthropomorphic hand, through the same shared interface. Our experiments show that Any-ttach improves tool-swapping reliability, increases demonstration efficiency, reduces tool-pose variability, and supports diverse tool-use skills. In two long-horizon tasks, making a sandwich and preparing a cucumber, Any-ttach executes six tool-use subskills through end-effector switching and execution monitoring. These results suggest that robots can expand manipulation capability not only through more complex end-effectors, but also through rapidly exchangeable tools and end-effector modules. More details and videos are available at https://any-ttach.github.io/.