The effect of methanol on the phase and phase-transition properties of a 2 × 8 ×8 glycerol-1-monopalmitate bilayer patch is investigated using a series of 239 molecular dynamics simulations on the 180 ns timescale, considering methanol concentrations cM and temperatures T in the ranges 0–12.3 M and 302–338 K, respectively. The results in the form of hysteresis-corrected transition temperatures Tm are compatible with the expected features of the biphasic effect, with a reversal concentration crev of about 5.2 M. Below this concentration, the main transition is between the liquid crystal (LC) and gel (GL) phases, and Tm decreases upon increasing cM. Above this concentration, the interdigitated (ID) phase is the stable ordered phase instead, and Tm slightly increases upon increasing T up to about 10 M. The analysis of the structural and dynamical properties also reveals very different sensitivities and responses of the three phases to changes in cM. In particular, the properties of the GL phase are insensitive to cM, whereas those of the LC and ID phases are altered via an increase of the area per lipid. For the LC phase, increasing cM promotes disorder and fluidity. For the ID phase, in contrast, increasing cM up to about 10 M slightly increases the ordering and rigidity. Two side issues are also addressed, concerning: (i) the occurrence tilt-precession motions in the GL and ID phases; (ii) the influence of the pressure coupling scheme employed in the simulations, semi- or fully-anisotropic, on the simulation results.