Influential slot and resource models of visual working memory make the assumption that items are stored in memory as independent units, and that there are no interactions between them. Consequently, these models predict that the number of items to be remembered (the set size) is the primary determinant of working memory performance, and therefore these models quantify memory capacity in terms of the number and quality of individual items that can be stored. Here we demonstrate that there is substantial variance in display difficulty within a single set size, suggesting that limits based on the number of individual items alone cannot explain working memory storage. We asked hundreds of participants to remember the same sets of displays, and discovered that participants were highly consistent in terms of which items and displays were hardest or easiest to remember. Although a simple grouping or chunking strategy could not explain this individual-display variability, a model with multiple, interacting levels of representation could explain some of the display-by-display differences. Specifically, a model that includes a hierarchical representation of items plus the mean and variance of sets of the colors on the display successfully accounts for some of the variability across displays. We conclude that working memory representations are composed only in part of individual, independent object representations, and that a major factor in how many items are remembered on a particular display is interitem representations such as perceptual grouping, ensemble, and texture representations.