We develop a Heterogeneous-Quantile Global VAR (HQGVAR) that allows each country-variable pair to enter the global system at its own quantile level. We provide a global admissibility result showing that we can assemble row-specific quantile equations into a stable reduced-form system with a valid moving-average representation and generalized impulse responses. The framework preserves the main structure of the GVAR but extends it to distributionally heterogeneous macro-financial environments. We establish large-sample theory for estimation and inference, justify moving-block bootstrap procedures, and show that the common-quantile QGVAR is a nested special case. Monte Carlo evidence demonstrates that heterogeneous-quantile modeling is valuable in the presence of heavy-tailed shocks, state-dependent spillovers, and asynchronous country-specific stress. In an application to a 13-economy macro-financial system, we do not reject system-wide equality with the median benchmark, but we detect localized, benchmark-referenced differences in financially and monetarily relevant transmission channels. Additional convergence, robustness, and forecast-validation diagnostics support the empirical implementation.