When two pre-existing, separated squares are connected by the sudden onset of a bar between them, viewers do not perceive the bar to appear all at once. Instead, they see an illusory morphing of the original squares over time. The direction of this transformational apparent motion (TAM) can be influenced by endogenous attention deployed before the appearance of the connecting bar. Here, we investigated whether the influence of endogenous attention on TAM results from operations over high-level feature-independent shape representations, or instead over lower level shape representations defined by specific visual features. To do so, we tested the influence of endogenous attention on TAM in first- and second-order displays, which shared common shapes but had different shape-defining attributes (luminance and texture contrast, respectively). In terms of both the magnitude of directional bias and timing, we found that endogenous attention exerted a similar influence on both first- and second-order objects. These results imply that endogenous attention biases the perceived direction of TAM by operating on high-level shape representations that are invariant to the low-level visual features that define them. Our results support a four-stage model of TAM, where a feature encoding stage passes a features-specific layout to a parsing stage that forms discrete, high-level meta-featural shapes, which are then matched and visually interpolated over time.