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System-level simulation and design space exploration (DSE) are key ingredients for the design of multiprocessor system-on-chip (MP-SoC) based embedded systems. The efforts in this area, however, typically use ad-hoc software infrastructures to facilitate and support the system-level DSE experiments. In this paper, we present a new, generic system-level MP-SoC DSE infrastructure, called NASA (Non Ad-hoc Search Algorithm). This highly modular framework uses well-defined interfaces to easily integrate different system-level simulation tools as well as different combinations of search strategies in a simple plug-and-play fashion. Moreover, NASA deploys a so-called dimension-oriented DSE approach, allowing designers to configure the appropriate number of, possibly different, search algorithms to simultaneously co-explore the various design space dimensions. As a result, NASA provides a flexible and re-usable framework for the systematic exploration of the multi-dimensional MP-SoC design space, starting from a set of relatively simple user specifications. To demonstrate the distinct aspects of NASA, we also present several DSE experiments in which we, e.g., compare NASA configurations using a single search algorithm for all design space dimensions to configurations using a separate search algorithm per dimension. These experiments indicate that the latter multi-dimensional co-exploration can find better design points and evaluates a higher diversity of design alternatives as compared to the more traditional approach of using a single search algorithm for all dimensions.