Recent studies have predicted a strong increase in high harmonic emission in unbiased semiconductor superlattices due to asymmetric current flow. In parallel, an external static bias has led to orders of magnitude control of high harmonics. Here, we study how this control can affect the operation of superlattice multipliers in a range of input frequencies and powers delivered by commercially available GHz sources. We show that the strongly nonlinear behavior can lead to a very complex scenario. Furthermore, it is natural to ask what happens when we combine both asymmetry and voltage control effects. This question is answered by the simulations presented in this study. The efficiency of high-order even harmonics is increased by the combined effects. Furthermore, the development of ‘petals’ in high-order emission is shown to be more easily achieved, opening the possibility to very interesting fundamental physics studies and more efficient devices for the GHz–THz range.