We investigated the sources of dual-task costs arising in multisensory working memory (WM) tasks, where stimuli from different modalities have to be simultaneously maintained. Performance decrements relative to unimodal single-task baselines have been attributed to a modality-unspecific central WM store, but such costs could also reflect increased demands on central executive processes involved in dual-task coordination. To compare these hypotheses, we asked participants to maintain two, three, or four visual items. Unimodal trials, where only this visual task was performed, and bimodal trials, where a concurrent tactile WM task required the additional maintenance of two tactile items, were randomly intermixed. We measured the visual and tactile contralateral delay activity (CDA/tCDA components) as markers of WM maintenance in visual and somatosensory areas. There were reliable dual-task costs, as visual CDA components were reduced in size and visual WM accuracy was impaired on bimodal relative to unimodal trials. However, these costs did not depend on visual load, which caused identical CDA modulations in unimodal and bimodal trials, suggesting that memorizing tactile items did not reduce the number of visual items that could be maintained. Visual load did not also affect tCDA amplitudes. These findings indicate that bimodal dual-task costs do not result from a competition between multisensory items for shared storage capacity. Instead, these costs reflect generic limitations of executive control mechanisms that coordinate multiple cognitive processes in dual tasks. Our results support hierarchical models of WM, where distributed maintenance processes with modality-specific capacity limitations are controlled by a central executive mechanism.