Some experiments with biological membranes have shown that a number of dopants can induce spontaneous lateral lipid separation into domains with different physical properties even in a monolipid membrane. Since most such dopants are approved drug substances, one can suppose this phenomenon is relevant to their therapeutic action. Such effect was observed for the dopants with bimodal adsorption. We assumed that the underlying mechanism of such dopant-induced domain formation is preferential dopant binding ‘like the surroundings′ rather than ‘unlike the surroundings′. In the present work, the simulation method based on the mechanism of preferential dopant binding to monolipid membrane has been developed. The domains sizes were calculated using a simple procedure similar to that used for percolation clusters. Using the method, the mean size of the largest lipid domains was shown to grow by orders of magnitude under moderate increase in the extent of preferential dopant binding. This finding affirms preferential binding as a governing mechanism of lipid domain formation in the systems explored. Adsorption isotherms for the case of bimodal sorption, albeit irrespective of surrounding, were analytically obtained. They coincide with the corresponding numerical simulation results. The method can be easily modified for exploring any systems with polymodal binding to a network of connected sites, so it may see increased application in the future for various physical, chemical, biological, biophysical and other systems.