The structures and electronic properties of a number of real and hypothetical ABX(2) compounds sharing (or evolving from) a single P4/mmm structural type are examined. These include the known CaCuO2 and SrFeO2 phases. A number of variations of this P4/mmm ABX(2) framework, some obvious, some exotic, all with a chemical motivation, were investigated: A = alkali metal, alkaline earth metal or La, B = Ti, Fe, Cu, or Pt, and X = C, O, S, C-2, H-2, or F. Careful attention was given to the d-orbital splitting patterns and magnetic states (ferromagnetic or antiferromagnetic) of these compounds, as well as their stability gauged by phonon dispersions and energetics. The most interesting as yet unmade compounds that emerged were (a) a carbide SrFe(C-2)(2), containing C-2 units with a C-C distance of 1.267 angstrom, (b) an AeTiO(2) series, with Ti-Ti bonding, part sigma, part pi, tuned by the Ae(2+) cation size, and (c) NaPtF2, for which a second structure was found, containing a hexagonal layering of (PtF2)(-) molecules.