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Extreme value applications commonly employ regression techniques to capture cross-sectional heterogeneity or time-variation in the data. Estimation of the parameters of an extreme value regression model is notoriously challenging due to the small number of observations that are usually available in applications. When repeated extreme measurements are collected on the same individuals, i.e., a panel of extremes is available, pooling the observations in groups can improve the statistical inference. We study three data sets related to risk assessment in finance, climate science, and hydrology. In all three cases, the problem can be formulated as an extreme value panel regression model with a latent group structure and group-specific parameters. We propose a new algorithm that jointly assigns the individuals to the latent groups and estimates the parameters of the regression model inside each group. Our method efficiently recovers the underlying group structure without prior information, and for the three data sets it provides improved return level estimates and helps answer important domain-specific questions.