We consider a system of weakly coupled bistable continuous stirred tank reactors. The number of reactors is larger than 2 and allows several stable nonuniform steady states. We investigate the mechanism leading to these steady states by analyzing numerically a model of coupled bistable chemical reactors. We show that multiple branches of stable and nonuniform steady states may coexist. Our analysis is motivated by a series of new experiments on a system of 16 coupled reactors distributed on a ring. Each reactor uses the bistable chlorite-iodide reaction. As a parameter is progressively changed, we observe cascading transitions to distinct nonuniform and symmetric steady states.