The pressure dependence of the superconducting transition temperature (T-c) and unit cell metrics of tetragonal (NH3)(y)Cs0.4FeSe were investigated in high pressures up to 41 GPa. The T-c decreases with increasing pressure up to 13 GPa, which can be clearly correlated with the pressure dependence of c (or FeSe layer spacing). The T-c vs. c plot is compared with those of various (NH3)(y)MxFeSe (M: metal atoms) materials exhibiting different T-c and c, showing that the T-c is universally related to c. This behaviour means that a decrease in two-dimensionality lowers the T-c. No superconductivity was observed down to 4.3 K in (NH3)(y)Cs0.4FeSe at 11 and 13 GPa. Surprisingly, superconductivity re-appeared rapidly above 13 GPa, with the T-c reaching 49 K at 21 GPa. The appearance of a new superconducting phase is not accompanied by a structural transition, as evidenced by pressure-dependent XRD. Furthermore, T-c slowly decreased with increasing pressure above 21 GPa, and at 41 GPa superconductivity disappeared entirely at temperatures above 4.9 K. The observation of a double-dome superconducting phase may provide a hint for pursuing the superconducting coupling-mechanism of ammoniated/non-ammoniated metal-doped FeSe.