In lipid membranes, temperature-induced transition from gel-to-fluid phase increases the lateral diffusion of the lipid molecules by three orders of magnitude. In cell membranes, a similar phase change may trigger the communication between the membrane components. Here concentration-induced phase transition properties of our recently developed statistical mechanical model of cholesterol/phospholipid mixtures are investigated. A slight (<1%) decrease in the model parameter values, controlling the lateral interaction energies, reveals the existence of a series of first- or second-order phase transitions. By weakening the lateral interactions first, the proportion of the ordered (i.e., superlattice) phase (Areg) is slightly and continuously decreasing at every cholesterol mole fraction. Then sudden decreases in Areg appear at the 0.18-0.26 range of cholesterol mole fractions. We point out that the sudden changes in Areg represent first- or second-order concentration-induced phase transitions from fluid to superlattice and from superlattice to fluid phase. Sudden changes like these were detected in our previous experiments at 0.2, 0.222, and 0.25 sterol mole fractions in ergosterol/DMPC mixtures. By further decreasing the lateral interactions, the fluid phase will dominate throughout the 0.18-0.26 interval, whereas outside this interval sudden increases in Areg may appear. Lipid composition-induced phase transitions as specified here should have far more important biological implications than temperature- or pressure-induced phase transitions. This is the case because temperature and pressure in cell membranes are largely invariant under physiological conditions.