In the context of robust optimization with information granules for distributional parameters, this paper investigates a two-stage waste-to-energy feedstock flow planning problem with uncertain capacity expansion costs. The objective is to minimize the worst-case overall loss in a mean-risk criterion where the risk is measured by a conditional value-at-risk operator. As a salient feature, an integrated uncertainty is considered which consists of not only the uncertainty in distribution shapes of the uncertain variables, but also the manifold uncertainties of the mean parameters. To tackle the robust optimization under such integrated uncertainty, we first discuss a distributional robust two-stage feedstock flow planning model with precise mean parameters that handles the uncertainty in distribution shape, and the model can be equivalently transformed into a linear program (LP). Furthermore, the precise-mean-based robust model is extended into the case of multifaceted uncertainty for mean-parameters that are allowed to assume intervals, historical-data-based probabilistic estimates, and/or human-knowledge-centric fuzzy set estimates, under different circumstances. These multifaceted uncertain mean-parameters are uniformly represented by using information granules, and a granular robust optimization model is then developed which maximizes the robustness of the solution within a shortfall tolerance, and realizes a tradeoff between the solution conservativeness and robustness. It is showed that the granular robust model is equivalent to solving a series of LPs and can be efficiently handled by a nested binary search algorithm. Finally, the computational study illustrates the model performance, solution analysis, and underlines a much higher scalability of the developed robust model compared to the stochastic programming approach.