The 9Ah battery upgrade will provide more ride time and mileage range however they will not make the scooter more powerful or faster.
The Razor E300 has a 24 Volt 250 Watt motor which is best suited for top speeds of around 12 to 15 mph. Its range tends to be between 5-10 miles depending on the terrain it is driven on and rider weight. To increase the top speed to 20 mph would require overvolting the original motor to 36 Volts or installing a more powerful motor and a smaller rear wheel chain sprocket.
Overvolting the original motor to 36 Volts would achieve the 20 mph goal with the least amount of effort and cost. The only downside of overvolting is that the motor will run hotter than normal which could sooner or later cause it to burn out. It all depends on how hot it gets though. Volts do not burn out motor only heat does - so as long as the motor does not get too hot then it will last a long time.
If you want to install a third battery to overvolt the scooter then all that would require is figuring out where to mount it, and using a 36 Volt battery charger to recharge the upgraded battery pack. The electronics of the scooter could be left alone or the controller could be upgraded to a 36 Volt unit at the same time that the battery pack is upgraded. The original 24 Volt controller usually works on 36 Volts however I have heard that some of the newest model controllers will not run on a higher Voltage battery pack. You would just have to try it and see how it goes.
Please let us know if you have any questions.