If you add a small car battery to the moped's existing battery
pack to increase the Voltage by 12 Volts that might increase the
maximum speed of the moped by overvolting the motor, or it might burn
out the controller and or motor from overvolting them.
If you decide to try this then a small car battery is not the right battery type to use because it is a starter battery and not a deep cycle battery. A starter battery would work for initial testing though, and could then be replaced with a deep cycle battery later on.
It is a fairly risky move to overvolt an electric moped. I would only
suggest doing this if you are prepared to replace the controller or
motor in case it does not work out.