The title compounds are obtained from reactions of the appropriate proportions of Sc, ScBr3, and elemental Z in sealed Nb tubing at 800--900 degrees C. The structures with Z = Mn, Ru, Os were established by single crystal means to be Sc-deficient examples of the Gd4I84+(Gd16I20Mn44-) structure (cubic P(4) over bar3$ m, Z = 1, a = 10.941(9), 10.9897(5), 11.0032(3) Angstrom) with 3.6(1), 3.0(1), and 2.9(1) scandium atoms in the tetrahedral cation portion, respectively. The cation deficiency with Z = Ru, Os affords 61-electron Sc(16)Br(20)Z(4) oligomeric units relative to the closed-shell expectation of 60 e(-). The dimensions, proportions, and bond orders in the Sc(16)Br(20)Z(4) oligomers (Sq symmetry) are compared with those in the four yttrium and one gadolinium examples previously known in this or other structure types. The Sc-Mn combination again displays the longest Sc-Z distances. A systematic breathing distortion of R(16)X(20)Z(4) clusters that increases in the order Y-I, Y-Br, Sc-Br(Ru,Os,Ir) to Sc-Br-Mn and Gd-I-Mn parallels many other comparisons. Extended Huckel MO calculations show these variations depend not only on relative atom sizes but also on appreciable variations in orbital energies and the resulting R-Z mixing in the frontier cluster orbitals (Kockerling and Martin, unpublished). Unusual variations in the magnetic susceptibilities of the Ru, Os examples over the range of 6-300 K are shown to be fit very well by a model based on a Boltzmann distribution of the odd electron between close-lying frontier al and tl orbitals with a temperature-dependent energy separation.