This paper studies extremal quantiles under two-way clustered dependence. We show that the limiting distribution of unconditional intermediate-order tail quantiles is Gaussian. This result is notable because two-way clustering typically leads to non-Gaussian limiting behavior. Remarkably, extremal quantiles remain asymptotically Gaussian even in degenerate cases. Building on this insight, we extend our analysis to extremal quantile regression at intermediate orders. Simulation results corroborate our theoretical findings. Finally, we provide an empirical application to growth-at-risk, showing that earlier empirical conclusions remain robust even after accounting for two-way clustered dependence in panel data and the focus on extreme quantiles.