To accomplish a 15-20 mph top speed and have hill climbing power a 1000 Watt motor would be needed. For a boost button what I recommend is to have a throttle output Voltage reduction circuit that reduces the throttle Voltage using a resistor and has an override switch to allow full throttle Voltage to the controller for the boost function. This will be much easier to do than to than to make a battery pack that switches from two batteries to three, or three to four. We sell a part that reduces the throttle Voltage and has a connector for a boost button. Its non boost mode can be fully adjusted with a screwdriver so the low speed can be anywhere between a crawl to full speed. It is our item # THR-ADJUSTER2 which is available on this page: https://cart.electricscooterparts.com/ProductDetails.asp?ProductCode=THR-ADJUSTER2
Here is a photo of it.
We can make a kit for your project if you would like. We would just need to know which parts to include with the kit. We can help with selecting the right sprockets so the quads have the right gear ratio for the top speed and hill climbing ability that you want. We can also help with selecting the right size batteries for the ride time that you want them to have. If you would like help with selecting the parts for your build then please let us know.