The phase relations within the system Tl2O3-BaO-CaO-CuO including Ag have been studied with emphasis on the high-temperature superconducting phases TIBa2Ca2Cu3O8.5 (1223 phase), Tl2Ba2Ca2Cu3O10 (2223 phase), TIBa2CaCu2O6.5 (1212 phase), and TI2Ba2CaCu2O8 (2212 phase) at 890 degreesC in an oxygen atmosphere. 1223 has been found to be in equilibrium with a liquid phase that is TI poor. 2223 and 2212 exhibit varying TI/(Ba + Ca) ratios. The three-phase field 1223 + 2223 + 2212 has been identified. The results of this study emphasize that multiphase samples can he prepared which consist of three superconducting phases, each exhibiting a critical temperature of 100 K or above.