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The research presented in this paper focuses on the effects of downsizing the electric motor drive of a fully electric vehicle through the adoption of a multiple-speed transmission system. The activity is based on the implementation of a simulation framework in Matlab / Simulink. The paper considers a rear wheel drive case study vehicle, with a baseline drivetrain configuration consisting of a single-speed transmission, which is compared with drivetrains adopting motors with identical peak power but higher base speeds and lower peak torques coupled with multiple-speed transmissions (double and three-speed), to analyze the benefits in terms of energy efficiency and performance. The gear ratios and gearshift maps for each multiple-speed case study are optimized through a procedure developed by the authors consisting of cost functions considering energy efficiency and performance evaluation. The cost functions are explained in the paper along with the models adopted for the research.