Mood, arousal, and other internal neural states can drastically alter behavior, even in identical external circumstances - the proverbial glass half full or empty. Neuromodulators are critical in controlling these internal neural states, and aberrations in neuromodulatory processes are linked to various neuropsychiatric disorders. To study how neuromodulators influence neural behavior, we modeled neuromodulation as a multiplicative factor acting on synaptic transmission between neurons in a recurrent neural network. We found this simple mechanism could vastly increase the computational capability and flexibility of a neural network by enabling overlapping storage of synaptic memories able to drive diverse, even diametrically opposed, behaviors. We analyzed how local or cell-type specific neuromodulation changes network activity to support such behaviors and reproduced experimental findings of Drosophila starvation behavior. We revealed that circuits have idiosyncratic, non-linear dose-response properties that can be different for chemical versus electrical modulation. Our findings help explain how neuromodulation "unlocks" specific behaviors with important implications for neuropsychiatric therapeutics.