The direct-site hypothesis assumes general anesthetics bind ion channels to impact protein equilibrium and function, inducing anesthesia. Despite advancements in the field, a first principle all-atom demonstration of this structure-function premise is still missing. We focus on the clinically used sevoflurane interaction to anesthetic-sensitive Kv1.2 mammalian channel to resolve if sevoflurane binds proteins well-characterized open and closed structures in a conformation-dependent manner to shift channel equilibrium. We employ an innovative approach relying on extensive docking calculations and free-energy perturbation of all potential binding sites revealed by the latter, and find sevoflurane binds open and closed structures at multiple sites under complex saturation and concentration effects. Results point to a non-trivial interplay of site and conformation-dependent modes of action involving distinct binding sites that increase channel open-probability at diluted ligand concentrations. Given the challenge in exploring more complex processes potentially impacting channel-anesthetic interaction, the result is revealing as it demonstrates the process of multiple anesthetic binding events alone may account for open-probability shifts recorded in measurements.