Resonance-like enhancements of generalized three-photon cross sections for extreme ultraviolet ionization of Ar, Kr, and Xe are demonstrated and analyzed within a single-active-electron, central-potential model. The resonant-like behavior is shown to originate from the potential barriers experienced by intermediate-and final-state photoelectron wave packets corresponding to absorption of one, two, or three photons. The resonance-like profiles in the generalized three-photon-ionization cross sections are shown to be similar to those found in the generalized two-photon-ionization cross sections [Phys. Rev. A 82, 053414 (2010)]. The complexity of Cooper minima in multiphoton-ionization processes is also discussed. Owing to the similar resonance-like profiles found in both two-and three-photon generalized cross sections, we expect such potential-barrier effects to be general features of multiphoton-ionization processes in most atoms with occupied p and d subshells.