We consider dynamic output feedback practical stabilization of uniformly observable nonlinear systems, based on high-gain observers with saturation. We assume that uncertain parameters and initial conditions belong to known but comparably large compact sets. In this situation, designs based on traditional robust or adaptive techniques, if applicable, would lead to high controller, observer, and adaptation gains. High gains may excite unmodeled dynamics and significantly amplify measurement noise. Moreover, they could be impossible or too costly to implement. In order to reduce the control efforts and improve robustness of a continuous high-gain-observer-based sliding mode control with respect to these nonideal operational conditions, we have recently proposed a new logic-based switching design strategy. In this paper, we generalize our technique and apply it to a wider class of nonlinear systems and more general Lyapunov-function-based state and output feedback designs. It is important to notice, in particular, that we require neither the sign of the high-frequency gain to be known nor the system to he minimum-phase. The key idea is to split the set of parameters into smaller subsets, design a controller for each of them, and switch the controller if the derivative of the Lyapunov function does not satisfy a certain inequality, after a dwell-time period. We do not order the candidate controllers in advance, as in our earlier work. Instead, we use estimates of the derivatives of the states, provided by an extended order high-gain observer, to calculate instantaneous performance indices. When the controller is falsified, we switch to a new controller that corresponds to the smallest index among the controllers that have not been falsified yet. This modification is important when the number of candidate controllers is high and pre-routed search may lead to an unacceptable transient performance.