Pressure has an essential role in the production(1) and control(2,3) 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(4,5). 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(1-3). 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 Tl0.6Rb0.4Fe1.67Se2, K0.8Fe1.7Se2 and K0.8Fe1.78Se2.