Stimuli-responsive metal-organic frameworks (MOFs) and other framework materials exhibit a broad variety of useful properties, which mainly stem from an interplay of strong covalent bonds within the organic linkers with presumably weak van der Waals (vdW) interactions which determine the overall packing of the framework constituents. Using Ag3Co(CN)6 as a fundamental test case-a system with a colossal positive and negative thermal expansion [A. L. Goodwin et al., Science 319, 794 (2008)]-we demonstrate that its structure, stability, dielectric, vibrational, and mechanical properties are critically influenced by many-body electronic correlation contributions to non-covalent vdW interactions. The Ag3Co(CN)6 framework is a remarkable molecular crystal, being visibly stabilized, rather than destabilized, by many-body vdW correlations. A detailed comparison with H3Co(CN)6 highlights the crucial role of strongly polarized metallophilic interactions in dictating the exceptional properties of denser MOFs. Beyond MOFs, our findings indicate that many-body electronic correlations can substantially stabilize polarizable materials, providing a novel mechanism for tuning the properties of nanomaterials with intricate structural motifs.