Conformal Risk Control (CRC) extends conformal prediction beyond the coverage setting to the control of general monotone loss functions, in a distribution-free and modelagnostic fashion. This makes it well-suited to problems with high-dimensional targets, such as the semantic segmentation task addressed in this work. However, CRC guarantees only marginal control, meaning that the risk is controlled on average over the data distribution. Under imbalanced distributions, the risk on inputs that contain rare objects may therefore remain uncontrolled, even when the marginal guarantee holds. We propose a new method that controls the risk on average over user-defined groups of the domain, drawing on Mondrian conformal prediction and macro-coverage algorithms. The method relies on a taxonomy, that is, a function that assigns a group to each data point, and reweights each point's risk by a coefficient that depends on its group probability, so that rare points contribute more than common ones. We illustrate the approach on two semantic segmentation datasets.

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