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This paper proposes interaction techniques for interactive reconfiguration of the transformation hierarchy among coordinate systems in the multi-viewport interface, which we have proposed for versatile three-dimensional (3-D) operations. The multi-viewport interface provides an arbitrary number of secondary views in window frames placed in a virtual environment, each showing the same or different virtual scenes from different perspectives. Using the multi-viewport interface, the user can seamlessly perform a variety of object manipulation and user navigation operations between multiple virtual scenes. The relationships among the reference frames of a window frame, the primary view outside the frame, the secondary view inside the frame, and the user define the characteristics and usability of a virtual environment; however, our former framework supports limited types of relationships and does not support interactive reconfiguration of the hierarchy. This paper extends our former framework with deeper analysis of combinations of the transformation hierarchy and a set of new interaction techniques for interactive reconfiguration of the hierarchy.