The clinical practice of selective serotonin reuptake inhibitor (SSRI) augmentation relies heavily on trial-and-error. Unfortunately, the drug combinations prescribed today fail to provide relief for many depressed patients. In order to identify potentially more effective treatments, we developed a computational model of the monoaminergic neurotransmitter and stress-steroid systems that neuroadapts to chronic administration of combinations of antidepressant drugs and hormones by adjusting the strengths of its transmitter-system components (TSCs). We used the model to screen 60 chronically administered drug/hormone pairs and triples, and identified as potentially therapeutic those combinations that raised the monoamines (serotonin, norepinephrine, and dopamine) but lowered cortisol following neuroadaptation in the model. We also evaluated the contributions of individual and pairs of TSCs to therapeutic neuroadaptation with chronic SSRI using sensitivity, correlation, and linear temporal-logic analyses. All three approaches revealed that therapeutic neuroadaptation to chronic SSRI is an overdetermined process that depends on multiple TSCs, providing a potential explanation for the clinical finding that no single antidepressant regimen alleviates depressive symptoms in all patients.