This study investigates the ability of the GW approximation to handle closed-shell multiferrence systems in their singlet ground state. Four scenarios are analyzed: the potential energy curve of BeH₂ during the insertion of a beryllium atom into a hydrogen molecule, the electron detachment and attachment energies of molecules with varying multiferrence character, the H₆ cluster with spin frustration, and the dissociation curve of the HF molecule. The results show that GW performs well in weakly correlated systems but has limitations in strongly correlated ones. The accuracy of GW depends on the level of self-consistency, the choice of initial guess, and the presence of spin-symmetry breaking. For BeH₂, GW provides a quantitative description except in regions of strong multiferrence character, where the agreement is qualitative. For molecules with varying multiferrence character, the optimal compromise is achieved with qsGW. The H₆ cluster demonstrates that breaking spin symmetry can be beneficial in certain contexts. The dissociation of HF shows that self-consistency and symmetry breaking can be useful for single-bond breaking processes, although the dissociation curve exhibits an unphysical "bump" near the Coulson-Fischer point. Overall, GW is effective for weakly correlated systems but requires further development to accurately describe strongly correlated systems. The study highlights the nuanced performance of GW for multiferrence chemical systems and suggests that explicit multiferrence implementations would be useful in certain chemical scenarios.This study investigates the ability of the GW approximation to handle closed-shell multiferrence systems in their singlet ground state. Four scenarios are analyzed: the potential energy curve of BeH₂ during the insertion of a beryllium atom into a hydrogen molecule, the electron detachment and attachment energies of molecules with varying multiferrence character, the H₆ cluster with spin frustration, and the dissociation curve of the HF molecule. The results show that GW performs well in weakly correlated systems but has limitations in strongly correlated ones. The accuracy of GW depends on the level of self-consistency, the choice of initial guess, and the presence of spin-symmetry breaking. For BeH₂, GW provides a quantitative description except in regions of strong multiferrence character, where the agreement is qualitative. For molecules with varying multiferrence character, the optimal compromise is achieved with qsGW. The H₆ cluster demonstrates that breaking spin symmetry can be beneficial in certain contexts. The dissociation of HF shows that self-consistency and symmetry breaking can be useful for single-bond breaking processes, although the dissociation curve exhibits an unphysical "bump" near the Coulson-Fischer point. Overall, GW is effective for weakly correlated systems but requires further development to accurately describe strongly correlated systems. The study highlights the nuanced performance of GW for multiferrence chemical systems and suggests that explicit multiferrence implementations would be useful in certain chemical scenarios.