Functional impairment after stroke is related to the amount of brain damage but there is no strict correspondence between lesion and magnitude of the deficit or its recovery. Theoretical constructs such as cognitive or brain reserve have been invoked as unspecific protective factors to explain this mismatch. Here, we consider the opposite point of view, that is the instances in which this protection is lost or overturned. Several studies have shown - in domains encompassing sensory, motor, and cognitive deficits - that paradigms in which the inherent processing limits of the brain are stressed (e.g., by introducing multitasking and attentional load), are indeed capable to unveil the presence of deficits that are otherwise missed. We administered a computerized multitasking paradigm to a sample of 46 consecutive patients with first-ever unilateral subacute to chronic stroke and no sign of lateralized spatial-attentional disorders according to established diagnostic tests. We then used cluster analysis to classify patients, in a purely data-driven manner, according to their multivariate pattern of performance across different conditions (e.g., single- vs dual-tasking, ipsi- vs. contra-lesional stimuli). This enabled us to identify, within a group of putatively spared patients, a cluster of individuals presenting with stark contralesional biases of spatial awareness exclusively in conditions of concurrent attentional load, i.e. a phenotype characterised by high susceptibility to multitasking. This construct was also captured by a latent factor obtained from principal component analysis, providing a continuous susceptibility index across the whole sample. In spite of similar lesion volume, patients in the high susceptibility cluster presented worse performance in activities of daily living and neuropsychological tests evaluating domain-general abilities spanning attention, executive functions, and reasoning. Multivariate predictive modeling based on lesions location and structural disconnections revealed distinctive correlates of high sensitivity to multitasking in the Multiple-Demand (MD) System, a network of frontal and fronto-parietal areas subserving domain general processes. Damage in these areas may critically interact with domain-specific ones (e.g., devoted to spatial attention), resulting in subtle, but significant difficulties for patients in everyday life situations. In conclusion, the construct of susceptibility to multitasking has the promising potential to provide us a better understanding of what marks the passage, after brain damage, to clinically visible deficits.