We report on the emergence of two disconnected superconducting domes in alkali-metal potassium- (K-)doped FeSe ultrathin films grown on graphitized SiC(0001). The superconductivity exhibits hypersensitivity to K dosage in the lower-T_{c} dome, whereas in the heavily electron-doped higher-T_{c} dome it becomes spatially homogeneous and robust against disorder, supportive of a conventional Cooper-pairing mechanism. Furthermore, the heavily K-doped multilayer FeSe films all reveal a large superconducting gap of ∼14 meV, irrespective of film thickness, verifying the higher-T_{c} superconductivity only in the topmost FeSe layer. The unusual finding of a double-dome superconducting phase is a step towards the mechanistic understanding of superconductivity in FeSe-derived superconductors.