Battery electric vehicles (BEVs) are a promising solution for reducing the impacts of passenger vehicles on the environment. However, their driving range is restricted due to the limitations of battery technologies. This range can be extended by adoption of multiple-speed transmissions. Most of the comparisons in the related studies are based on non-optimal designs or limited to modal driving cycles. Furthermore, the impact of power-split continuously variable transmission (PS-CVT) layout with type III power flow on the power consumption of BEVs has never been examined. In this paper, single, two and three-speed transmissions along with PS-CVTs with type I and III power flows are optimized for a case study BEV. Furthermore, the effect of push belt and full-toroidal CVTs in construction of PS-CVT are compared. The results demonstrate that a PS-CVT with type I power flow equipped with the full-toroidal CVT has the best performance. However, it reduces the energy consumption by 0.36% compared to the optimal two-speed layout. In addition, its ratio range is more limited which can negatively impact the dynamic performance. Finally, simulation of the optimal designs along a different cycle proves that the obtained results are consistent, regardless of the driving cycle.