The ternary compounds K34In91.05(9)Mg13.95(9) (I), K34In96.19(6) Au-8.81(6) (II), and K34In89.95(1) Zn-13.05(7) (III) have been synthesized by high-temperature means and structurally characterized by single-crystal X-ray diffraction methods. All are analogues of earlier products in which Li is substituted for some In in a hypothetical K34In105 lattice. They consist of complex three-dimensional anionic networks built of In-12 icosahedra and M-28 triply fused icosahedra (M = In or In/T and T = Mg, Au, or Zn). The K atoms bridge between cluster faces or edges and form K-136 clathrate-II type networks. Two neighboring M-28 units are interconnected by an M atom to form a sandwich complex (M-28)M-(M-28) in I and II or by a Zn-Zn dimer in (M-28)ZnZn(M-28) in III. Mixed In/T sites only occur in the M-28 portions. Phase stabilization through electronic tuning is present in all three via substitution of the electron-poorer T elements for In. Extended Huckel analyses indicate that all metal-metal bonding within the M-28 cluster appears to be optimized in I and III even though both are metallic. The size of the substituted element is also important in the structural features, as is especially shown by the Zn compound.