Inflatable structures have become essential components in the design of soft robots and deployable systems as they enable dramatic shape change from a single pressure inlet. This simplicity, however, often brings a strict limitation: unimodal deformation upon inflation. Here, multistability is embraced to design modular, inflatable structures that can switch between distinct deformation modes as a response to a single input signal. This system comprises bistable origami modules in which pressure is used to trigger a snap-through transition between a state of deformation characterized by simple deployment to a state characterized by bending deformation. By assembling different modules and tuning their geometry to cause snapping at different pressure thresholds, structures capable of complex deformations that can be preprogrammed and activated using only one pressure source are created. This approach puts forward multistability as a paradigm to eliminate a one-to-one relation between input signal and deformation mode in inflatable systems.

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