This paper studies the global asymptotic stabilization of passive nonlinear systems with finite, countable control actions. We show that for nonlinear passive systems that are large-time norm observable and admit a finite control input set whose convex hull contains the origin, the origin can be globally asymptotically stabilized and locally exponentially stabilized by means of relaxed control and nearest-action control approaches. In particular, we improve on a recent result of practical stabilization via nearest-action control by utilizing switching controllers that can synthesize extra control actions from an existing control input set. Three switching methodologies are proposed to enlarge the control set and enable global asymptotic and local exponential stabilization. These three methodologies vary in the cardinality of the expanded control set. These methods are validated in numerical simulations where a comparison of the convergence rate is provided.