Biomolecular receptors are able to process information by responding differentially to combinations of chemical signals. Synthetic receptors that are likewise capable of multi-stimuli response can form the basis of programmable molecular systems, wherein specific input sequences create distinct outputs. Here we report a pseudo-cuboctahedral assembly capable of cooperatively binding anionic and neutral guest species. The binding of pairs of fullerene guests was observed to effect the all-or-nothing cooperative templation of an S6-symmetric host stereoisomer. This bis-fullerene adduct exhibits different cooperativity in binding pairs of anions from the fullerene-free parent: in one case, positive cooperativity is observed, while in another all binding affinities are enhanced by an order of magnitude, and in a third the binding events are only minimally perturbed. This intricate modulation of binding affinity, and thus cooperativity, renders our new cuboctahedral receptor attractive for incorporation into systems with complex, programmable responses to different sets of stimuli.