The pressure dependence of the superconducting transition temperature (Tc) and unit cell metrics of tetragonal (NH3)yCs0.4FeSe were investigated in high pressures up to 41 GPa. The Tc decreases with increasing pressure up to 13 GPa, which can be clearly correlated with the pressure dependence of c (or FeSe layer spacing). The Tc vs. c plot is compared with those of various (NH3)yMxFeSe (M: metal atoms) materials exhibiting different Tc and c, showing that the Tc is universally related to c. This behaviour means that a decrease in two-dimensionality lowers the Tc. No superconductivity was observed down to 4.3 K in (NH3)yCs0.4FeSe at 11 and 13 GPa. Surprisingly, superconductivity re-appeared rapidly above 13 GPa, with the Tc 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, Tc 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.