Self-assembled nanoparticle superlattices-materials made of inorganic cores capped by organic ligands, of varied structures, and held together by diverse binding motifs-exhibit size-dependent properties as well as tunable collective behaviour arising from couplings between their nanoscale constituents(1-15). Here, we report the single-crystal X-ray structure of a superlattice made in the high-yield synthesis(16) of Na4Ag44(p-MBA)(30) nanoparticles, and find with largescale quantum-mechanical simulations that its atomically precise structure and cohesion derive from hydrogen bonds between bundled(4) p-MBA ligands. We also find that the superlattice's mechanical response to hydrostatic compression is characterized by a molecular-solid-like bulk modulus B-0 =16.7 GPa, exhibiting anomalous pressure softening and a compression-induced transition to a soft-solid phase. Such a transition involves ligand flexure, which causes gear-like correlated chiral rotation of the nanoparticles. The interplay of compositional diversity, spatial packing efficiency, hydrogen-bond connectivity, and cooperative response in this system exemplifies the melding of the seemingly contrasting paradigms of emergent behaviour 'small is different'(9) and 'more is different'(17).