In this work, we seek to elucidate a common stabilization principle for the metastable and equilibrium phases of the Al-Mg-Si-Cu alloy system, through combined experimental and theoretical studies. We examine the structurally known well-ordered Al-Mg-Si-Cu alloy metastable precipitates along with experimentally observed disordered phases, using high angle annular dark field scanning transmission electron microscopy. A small set of local geometries is found to fully explain all structures. Density functional theory based calculations have been carried out on a larger set of structures, all fully constructed by the same local geometries. The results reveal that experimentally reported and hypothetical Cu-free phases from the set are practically indistinguishable with regard to formation enthalpy and composition. This strongly supports a connection of the geometries with a bulk phase stabilization principle. We relate our findings to the Si network substructure commonly observed in all Mg-Al-Si(-Cu) metastable precipitates, showing how this structure can be regarded as a direct consequence of the local geometries. Further, our proposed phase stabilization principle clearly rests on the importance of metal-Si interactions. Close links to the Al-Mg-Si precipitation sequence are proposed.