Dual–Primal FETI (FETI-DP) is a widely used non-overlapping domain decomposition method combining robustness with excellent parallel scalability. In the presence of strong coefficient heterogeneity—particularly when large jumps align with subdomain interfaces—the convergence of the preconditioned interface operator can deteriorate markedly. Although advanced scaling strategies (e.g., ρ- and Deluxe-scaling) alleviate part of this effect, they do not, in general, prevent the onset of ill-conditioning driven by localized interface modes. Robustness is then recovered by enriching the coarse space beyond the standard primal set (typically corners). A systematic and provably robust enrichment is provided by adaptive coarse spaces pioneered by Mandel and Sousedík, where problematic interface components are identified by solving local generalized eigenvalue problems (GEVPs) and promoting selected eigenmodes to primal constraints. The practical limitation is cost: solving a GEVP on each interface can dominate setup time, so that “full adaptivity” is often not viable in large-scale or many-query settings. We propose RB-GEVP, a reduced-basis strategy that accelerates adaptive coarse-space construction by exploiting the structure imposed by coefficient distributions along interfaces. Building on heuristics such as Frugal FETI-DP, we construct a coefficient-aware reduced space for each interface and solve the adaptive GEVP only in this reduced space. This approach yields projected eigenproblems that are orders of magnitude smaller while preserving the ability to detect the critical interface modes responsible for condition-number growth. The selected projected eigenvectors are then used to define additional primal constraints, producing an enriched coarse space comparable in quality to full adaptivity. Numerical experiments ranging from academic high-contrast binary distributions to interface patterns arising in modular topology optimization show that RB-GEVP achieves near-equivalent mode selection and condition-number stabilization relative to full adaptive FETI-DP, at a fraction of the eigenanalysis cost, thereby improving overall time-to-solution.