Alkali copper sulfates form a rapidly developing family of inorganics. Herein, we report synthesis and crystal structure, and evaluate possible ion migration pathways for a novel Na-K-Cu anhydrous sulfate, K(Na,K)Na2[Cu2(SO4)4]. The CuO7 and SO4 polyhedra share common vertices and edges to form [Cu2(SO4)4]4− wide ribbons, which link to each other via common oxygen atoms forming the host part of the structure. Four guest alkali sites are occupied by solely K+, mixture of K+ and Na+, and solely Na+, which agrees well with the size of the cavities. The crystal structure of K(Na,K)Na2[Cu2(SO4)4] contains two symmetry-independent Cu sites with [4+1+(2)] coordination environments. The overall coordination polyhedra of Cu2+ can be considered as `octahedra with one split vertex'. A similar coordination mode was observed also in some other multinary copper sulfates, mostly of the mineral world. These coordination modes were reviewed and five types of CuO7 polyhedra are identified. CuO7 polyhedra are almost restricted to copper sulfates and phosphates. It was found that a larger amount of the smaller SO4
2− and PO4
3− anions can cluster around a single Cu2+ cation; in addition, for such relatively small anions, both mono (κ1) and bidentate (κ2) coordination modes to the Cu2+ are possible. The correlation between crystallographic characteristics and bond valence energies showed that the new copper sulfate framework, [Cu2(SO4)4]4−, contains one interconnected path suitable for Na+ mobility at tolerable activation energies and that K(Na,K)Na2[Cu2(SO4)4] can be considered as a potential candidate for novel Na-ion conductors.