Most investigations of visual search have focused on the discrimination between a search target and other task-irrelevant distractor objects (selection). The attentional limitations that arise when multiple target objects in the same display have to be processed simultaneously (access) remain poorly understood. Here, we employed behavioral and electrophysiological measures to investigate the factors that determine whether multiple target objects can be accessed in parallel. Performance and N2pc components were measured for search displays that contained either a single target or two target objects. When two target objects were present, they either had the same or different target-defining features. Participants reported whether search displays contained a single target, two targets with shared features, or two targets with different features. There were performance costs as well as reduced N2pc amplitudes for two-target/different relative to two-target/same displays, suggesting that access to multiple target objects defined by different features was impaired. These behavioral and electrophysiological costs were also observed in a task where all search display objects were physically different, but not during color or shape singleton search, confirming that they do not reflect a low-level perceptual grouping of physically identical targets. These results demonstrate strong feature-specific limitations of visual access, as proposed by the Boolean map theory of visual attention. They suggest that multiple target objects can be accessed in parallel only when they share task-relevant features and demonstrate that mechanisms of visual access can be studied with electrophysiological markers.