Membrane proteins are primary targets for most therapeutic indications in cancer and neurological diseases, binding over 50% of all known small molecule drugs. Understanding how such ligands impact membrane proteins requires knowledge on the molecular structure of ligand binding, a reasoning that has driven relentless efforts in drug discovery and translational research. Binding of small ligands appears however highly complex involving interaction to multiple transmembrane protein sites featuring single or multiple occupancy states. Within this scenario, looking for new developments in the field, we investigate the concentration-dependent binding of ligands to multiple saturable sites in membrane proteins. The study relying on docking and free-energy perturbation provides us with an extensive description of the probability density of protein-ligand states that allows for computation of thermodynamic properties of interest. It also provides one- and three-dimensional spatial descriptions for the ligand density across the protein-membrane system which can be of interest for structural purposes. Illustration and discussion of the results are shown for binding of the general anesthetic sevoflurane against Kv1.2, a mammalian ion channel for which experimental data are available.