TURBO BUTTON

Not really. There are two types of brushless motors, AC and DC.

AC needs a controller to convert the DC power of the batteries to steady AC.

Even though the DC's are called "DC brushless motors" in reallity they use a kind of what you could say is essencially a complex 3-phase AC current. So you need some kind of controller for either kind of brushless motor.

Now one thing that could be possible to give it more speed is increasing the voltage, either by more batteries or battery cells in a series, or a voltage converter. But that in turn could damage the motor and/or controller so you may have to change those too. A higher amp drawing motor would also put out more power but you would maybe have to add more batteries as well as a controller that can handle the amps. Gear ratio or wheel diameter could possibly change top speed in exchange for torque (acceleration).

Brushed DC motors can be connected directly to the battery with no need of a controller. (But still I wouldn't recomend it.)

Personnally I don't see how a motor directly connected to a battery would in itself have any significant effect on the vehicle's speed. Your controller's top output voltage should equil that of you battery pack. Now if you have a problem with the controller malfunctioning then you need a new controller, not a direct connection.

the only other thing I can think of is to somehow get more amperage to the motor.
Basically the same way that people have modified the shunt in the xb-500/600 controllers.
I have an xb-600 that i upgraded to 60V with the shunt mod and I also have a push button switch installed so that the limiting governor is in effect limiting the speed to 20mph when active and going up to 29mph when not active.

Where is the push-button connected, into the controller?
Near the shunts?
Thanks.