Pressure has an essential role in the production and control of superconductivity in iron-based superconductors. Substitution of a large cation by a smaller rare-earth ion to simulate the pressure effect has raised the superconducting transition temperature T(c) to a record high of 55 K in these materials. In the same way as T(c) exhibits a bell-shaped curve of dependence on chemical doping, pressure-tuned T(c) typically drops monotonically after passing the optimal pressure. Here we report that in the superconducting iron chalcogenides, a second superconducting phase suddenly re-emerges above 11.5 GPa, after the T(c) drops from the first maximum of 32 K at 1 GPa. The T(c) of the re-emerging superconducting phase is considerably higher than the first maximum, reaching 48.0-48.7 K for Tl(0.6)Rb(0.4)Fe(1.67)Se(2), K(0.8)Fe(1.7)Se(2) and K(0.8)Fe(1.78)Se(2).