This paper describes a flexible and efficient new algorithm for model order reduction of parameterized systems. The method is based on the reformulation of the parameterized system as a perturbation-like parallel interconnection of the nominal transfer function and the nonparameterized transfer function sensitivities with respect to the parameter variations. Such a formulation reveals an explicit dependence on each parameter which is exploited by reducing each component system independently via a standard nonparameterized structure preserving algorithm. Therefore, the resulting smaller size interconnected system retains the structure of the original system with respect to parameter dependence. This allows for better accuracy control, enabling independent adaptive order determination with respect to each parameter and adding flexibility in simulation environments. It is shown that the method is efficiently scalable and preserves relevant system properties such as passivity. The new technique can handle fairly large parameter variations on systems whose outputs exhibit smooth dependence on the parameters, also allowing design space exploration to some degree. Several examples show that besides the added flexibility and control, when compared with competing algorithms, the proposed technique can, in some cases, produce smaller reduced models with potential accuracy gains.