A double-walled tetrahedral metal-organic cage assembled in solution from silver(I), 2-formyl-1,8-naphthyridine, halide, and a threefold-symmetric triamine. The AgI4X clusters at its vertices bring together six naphthyridine-imine moieties, leading to a structure in which eight tritopic ligands bridge four clusters in an (AgI4X)4L8 arrangement. Four ligands form an inner set of tetrahedron walls that are surrounded by the outer four. The cage has significant interior volume, and was observed to bind anionic guests. The structure also possesses external binding clefts, located at the edges of the cage, which bound small aromatic guests. Halide ions bound to the silver clusters were observed to exchange in a well-defined hierarchy, allowing modulation of the cavity volume. The principles uncovered here may allow for increasingly more sophisticated cages with silver-cluster vertex architectures, with post-assembly tuning of the interior cavity volume enabling targeted binding behavior.