Important features of the internal chemistry of the quadruple perovskite family of layered cuprates, such as solid solution behavior, stable defect species, and oxidation behavior, have been investigated by structural and physical property measurements and related to the inner architecture of these potential superconductors, In-situ high-temperature (650-800 degrees C) electrical conductivity and Seebeck coefficient measurements have been performed, in various oxygen partial pressures, on pure and chemically substituted Ln’Ln"Ba2Cu2Ti2O11 (Ln’Ln" = LaY or NdDy) compounds. The electrical properties display transitions from dual carrier (intrinsic) semiconductivity to extrinsically doped p-type semiconductivity as a function of chemical composition, temperature, and oxygen pressure. The exclusion of interstitial oxygen defects between the copper-oxygen double layers, as evidenced in the weak oxygen partial pressure dependence of the electrical properties in the LaYBa2Cu2Ti2O11 systems, is directly related to the A-site order and is an important step toward achieving superconductivity by preserving the structural integrity of the CuO22- planes. The electrical properties of the NdDy system, however, are strong functions of the oxygen partial pressure, indicating that oxygen defects play an important role in determining their properties. Oxidation of the latter compound has been achieved, and underdoped metallic behavior reminiscent of known superconductors has been observed at low temperatures (100-300 K). Jonker analysis of the electrical properties of the highly oxidized material further illustrates the similarity of the transport behavior of the quadruple perovskites to superconducting cuprates. A combination of synthesis and annealing methods which allow for both increased substitution levels and carrier concentrations should lead to superconductivity in the ordered-lanthanide quadruple perovskites.