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Approximate computing appears as an emerging and promising solution for energy-efficient system designs, exploiting the inherent error-tolerant nature of various applications. In this paper, targeting multiplication circuits, i.e., the energy-hungry counterpart of hardware accelerators, an extensive exploration of the errorś energy trade-off, when combining arithmetic-level approximation techniques, is performed for the first time. Arithmetic-aware approximations deliver significant energy reductions, while allowing to control the error values with discipline by setting accordingly a configuration parameter. Inspired from the promising results of prior works with one configuration parameter, we propose 5 hybrid design families for approximate and energy-friendly hardware multipliers, consisting of two independent parameters to tune the approximation levels. Interestingly, the resolution of the state-ofthe-art Pareto diagram is improved, giving the flexibility to achieve better energy gains for a specific error constraint imposed by the system. Moreover, we outperform prior works in the field of approximate multipliers by up to 60% energy reduction, and thus, we define the new Pareto front.