The search for biological causes of mental disorders has up to now met with limited success, leading to growing dissatisfaction with diagnostic classifications. However, it is questionable whether most clinical syndromes should be expected to correspond to specific microscale brain alterations, as multiple low-level causes could lead to similar symptoms in different individuals. In order to evaluate the potential multifactoriality of alterations related to psychiatric illness, we performed a parametric exploration of published computational models of schizophrenia. By varying multiple parameters simultaneously, such as receptor conductances, connectivity patterns, and background excitation, we generated 5625 different versions of an attractor-based network model of schizophrenia symptoms. Among networks presenting activity within valid ranges, 154 parameter combinations out of 3002 (5.1%) presented a phenotype reminiscent of schizophrenia symptoms as defined in the original publication. We repeated this analysis in a model of schizophrenia-related deficits in spatial working memory, building 3125 different networks, and found that 41 (4.9%) out of 834 networks with valid activity presented schizophrenia-like alterations. In isolation, none of the parameters in either model showed adequate sensitivity or specificity to identify schizophrenia-like networks. Thus, in computational models of schizophrenia, even simple network phenotypes related to the disorder can be produced by a myriad of causes at the molecular and circuit levels. This suggests that unified explanations for either the full syndrome or its behavioral and network endophenotypes are unlikely to be expected at the genetic and molecular levels.