The high-temperature electrical conductivity and thermopower of several compounds in the In2O3(ZnO)k system (k=3, 5, 7, and 9) were measured, and the band structures of the k=1, 2, and 3 structures were predicted based on first-principles calculations. These phases exhibit highly dispersed conduction bands consistent with transparent conducting oxide behavior. Jonker plots (Seebeck coefficient versus natural logarithm of conductivity) were used to obtain the product of the density of states and mobility for these phases, which were related to the maximum achievable power factor (thermopower squared times conductivity) for each phase by Ioffe analysis (maximum power factor versus Jonker plot intercept). With the exception of the k=9 phase, all other phases were found to have maximum predicted power factors comparable to other thermoelectric oxides if suitably doped.