The ultrahigh porosity and varied functionalities of porous metal-organic frameworks make them excellent candidates for applications that range widely from gas storage and separation to catalysis and sensing. An interesting feature of some frameworks is the ability to open their pores to a specific guest, enabling highly selective separation. A prerequisite for this is bistability of the host structure, which enables the framework to breathe, that is, to switch between two stability minima in response to its environment. Here we describe a porous framework DUT-8(Ni)-which consists of nickel paddle wheel clusters and carboxylate linkers-that adopts a configurationally degenerate family of disordered states in the presence of specific guests. This disorder originates from the nonlinear linkers arranging the clusters in closed loops of different local symmetries that in turn propagate as complex tilings. Solvent exchange stimulates the formation of distinct disordered frameworks, as demonstrated by high-resolution transmission electron microscopy and diffraction techniques. Guest exchange was shown to stimulate repeatable switching transitions between distinct disorder states.