Second-line depression treatment involves augmentation with one (rarely two) additional drugs, of chronic administration of a selective serotonin reuptake inhibitor (SSRI), which is the first-line depression treatment. Unfortunately, many depressed patients still fail to respond even after months to years of searching to find an effective combination. To aid in the identification of potentially affective antidepressant combinations, we created a computational model of the monoaminergic neurotransmitter (serotonin, norepinephrine, and dopamine), stress-hormone (cortisol), and male sex-hormone (testosterone) systems. The model was trained via machine learning to represent a broad set of empirical observations. Neuroadaptation to chronic drug administration was simulated through incremental adjustments in model parameters that corresponded to key regulatory components of the neurotransmitter and neurohormone systems. Analysis revealed that neuroadaptation in the model depended on all of the regulatory components in complicated ways, and did not reveal any one or a few specific components that could be targeted in the design of combination antidepressant treatment. We used large sets of neuroadapted states of the model to screen 74 different drug and hormone combinations and identified several combinations that could potentially be therapeutic for a higher proportion of male patients than SSRIs by themselves.