It is geometrically feasible to insert metal-metal-bonded M(4) tetrahedra and M(6) octahedra into the tetrahedral and octahedral holes, respectively, of the fee C-60 lattice. The electronic structure of the hypothetical tetrahedral variants C-60(M(4))(2). M = Rh, Co, is analyzed with approximate molecular orbital methods and band structure calculations. These compounds feature M-M and M-C-60 bonding and a variable degree of electron transfer to or from C-60. The C-60(M(4))(2) phases should be metallic, but we have no way of predicting if they will be superconducting. A number of discrete molecular tetrahedral cluster compounds which serve as models for the solid state materials are analyzed. There is a clear indication that tetranuclear and even mononuclear Rh, Ir, and Co arene complexes should be relatively unstable.