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Among the iron-based superconductors, the structural simplest FeSe and its derived materials have received much attention in recent years due to the great tunability of the superconducting transition temperature (Tc). The relatively low Tc 8.5 K of FeSe can be raised to over 40 K via the interlayer intercalations such as AxFe2-ySe2 (A=K, Rb, Cs, Tl), Lix(NH3)yFe2Se2, and (Li1-xFex)OHFeSe. Although the monolayer FeSe/SrTiO3 is reported to have a Tc as high as 65 K, none of the Tc values of these FeSe-derived bulk materials has exceeded 50 K at ambient pressure so far. In order to explore other routes to further enhance Tc of FeSe-based materials, we recently performed the detailed high-pressure study of two intercalated FeSe high-Tc superconductors, namely (Li0.84Fe0.16)OHFe0.98Se and Li036(NH3)yFe2Se2, by using a cubic anvil cell apparatus. We find that the applied high pressure first suppresses the superconducting phase (denoted as SC-I) and then induces a second high-Tc superconducting phase (denoted as SC-Ⅱ) above a critical pressure Pc (~5 GPa for (Li0.84Fe0.16)OHFe0.98Se and 2 GPa for Li036(NH3)yFe2Se2). The highest Tc values in the SC-Ⅱ phases of these two compounds can reach~52 K and 55 K, respectively, the latter of which is the highest in the FeSe-based bulk materials, and is very close to the highest Tc of FeAs-based high-Tc superconductors. Our high-precision resistivity data of (Li0.84Fe0.16)OHFe0.98Se also uncover a sharp transition of the normal state from Fermi liquid for SC-I to non-Fermi liquid for SC-Ⅱ phase. In addition, the reemergence of high-Tc SC-Ⅱ phase under pressure is found to be accompanied with a concurrent enhancement of electron carrier density. Interestingly, we find a nearly parallel scaling behavior between Tc and the inverse Hall coefficient for the SC-Ⅱ phases of both (Li0.84Fe0.16)OHFe0.98Se and Li0.36(NH3)yFe2Se2. In the case without structural transition below 10 GPa, the observed enhancement of carrier density in SC-Ⅱ should be ascribed to an electronic origin presumably associated with pressure-induced Fermi surface reconstruction. Our work demonstrates that high pressure offers a distinctive means to further raise the maximum Tc values of intercalated FeSe-based materials.