Brain electrical stimulation (BES) has long been suggested as a means of controlling pathological brain activity. In epilepsy, control of a spatially localized source, the seizure focus, may normalize neuronal dynamics. Consequently, most BES research has been directed at controlling small, local, neuronal populations. At a higher level, pathological seizure activity can be viewed as a network event that may begin without a clear spatial focus or in multiple sites and spread rapidly through a distributed cortical network. In this paper, we begin to address the implications of local control in a network scenario. To do so, we explore the efficacy of local BES when deployed over a larger-scale neuronal network, for instance, using a grid of stimulating electrodes on the cortex. By introducing a mean-field model of neuronal interactions we are able to identify limitations in network controllability based on physiological constraints that suggest the need for more nuanced network control strategies.