When performing tasks using computers, multiple documents are used with multiple applications. During working with computers, multiple tasks, perhaps involving multiple documents, are switched. This paper presents the Docking Window Framework: an extended multi-window system supporting such multitasking situations. It enables construction of workspaces comprising multiple windows with simple switching of workspaces. Although previous systems emphasized the support of task-switching after workspace construction, the proposed system characteristically supports construction of workspaces through a docking user interface. It also supports operation of multiple windows simultaneously, provides a tile layout of windows to reduce the overhead of window operations, and supports saving and restoration of workspaces. We conducted two experiments to evaluate the system. In window arrangement tasks, participants performed tasks faster using the proposed system than when using a popular window system (Windows XP). Moreover, in task-switching tasks, participants using our system performed multiple tasks in parallel more efficiently.