Covalent post-assembly modification (PAM) reactions are useful synthetic tools for functionalizing and stabilizing self-assembled metal-organic complexes. Recently, PAM reactions have also been explored as stimuli for triggering supramolecular structural transformations. Herein we demonstrate the use of inverse electron-demand Diels-Alder (IEDDA) PAM reactions to induce supramolecular structural transformations starting from a tetrazine-edged (Fe4L6)-L-II tetrahedral precursor. Following PAM, this tetrahedron rearranged to form three different architectures depending on the addition of other stimuli: an electron-rich aniline or a templating anion. By tracing the stimulus-response relationships within the system, we deciphered a network of transformations that mapped different combinations of stimuli onto specific transformation products. Given the many functions being developed for self-assembled three-dimensional architectures, this newly established ability to control the interconversion between structures using combinations of different stimulus types may serve as the basis for switching the functions expressed within a system.