The complex functions of neuronal synapses in the central nervous system depend on their tightly interacting, compartmentalized molecular network of hundreds of proteins spanning the pre- and post-synaptic sites. This biochemical system is implicated in the pathogenesis of autism spectrum disorders and schizophrenia, with identified common synaptopathologies and numerous risk genes associated with synaptic function. However, it remains unclear how the synaptic molecular network is altered in these disorders, and whether effects are common to distinct genetic perturbations. Here, we applied PRISM, a quantitative single-synapse multiplexed imaging technique, to systematically probe the effects of RNAi knockdown of 16 autism- and schizophrenia-associated genes on the simultaneous distribution of 10 synaptic proteins. This enabled the identification of novel phenotypes in synapse compositions and distributions. We applied Bayesian network inference to construct and validate a predictive model of causal hierarchical dependencies among eight proteins of the excitatory synapse. The resulting conditional dependence relationships could only be accessed via measurement which is both single-synapse and multiprotein, unique to PRISM. Finally, we show that central features of the network are similarly affected across distinct gene knockdowns. These results offer insight into the convergent molecular etiology of these debilitating, hereditary and highly polygenic disorders, as well as offering a novel, general framework for probing subcellular molecular networks.