We investigated complex magnetic domain formation on a chiral molecule-based magnet, [Cr(CN)6][Mn(R)-pnH(H2O)](H2O) (termed as R-GN), whose two-dimensional molecular network was constructed with the help of a single-handed chiral ligand ((R)-pn). There, the first- and third-harmonic magnetic responses (M1ω and M3ω) against the ac magnetic field were observed, and magnetic hysteresis in ac field of a few Oe was discussed in terms of Rayleigh loop. The diagnostics of this magnetic hysteresis clarified the complex process of magnetic domain formation against a change in temperature. For R-GN, it was reported that a giant M3ω (termed #4 in this paper) appeared just above the so-called “magnetic ordering temperature (TC).” In the present study, three M3ω responses (#1-3) were newly observed on the lower-temperature side of #4, and the ac field dependencies for all of #1-#4 were investigated. #1 also accompanied the giant M3ω, which suggests that a significant degree of magnetic fluctuation surviving below TC. This glassy behavior below TC is an attractive new phenomenon in molecule-based magnets with a single-handed chiral ligand. #2 and #3 exhibited magnetic ordering and the formation of a small magnetic domain, respectively. The M3ω responses of #1-3 were suppressed with increasing the amplitude of ac field, and the corresponding magnetic hysteresis was a normal Rayleigh loop accompanying the out-of-phase of the M1ω response. The M3ω response of #4 without the out-of-phase of M1ω was, however, enhanced with increasing the amplitude of ac field, and #4 represented a large magnetic hysteresis in the paramagnetic region, intrinsically different from those of #1-#3.