The alternator that you have at the moment is 150 A, so at 14 V the power is 2100 W. That is the most that can be got from it. Obviously the car's systems will take some power, maybe 20 A without the AC or any lights on, and if the engine is at tickover, you probably won't get more than about 80 A from the alternator, leaving maybe 60A available.
For short term power, the battery will provide that, although the voltage will dip once you start taking current from the alternator.
Also, if the power load is fluctuating, car alternators are slow to respond, so for the battery is needed to supply power when the load increases suddenly, and to absorb power when the load reduces suddenly. Every time the fan starts, or the heated screen turns on, or the headlights are turned on, it's the battery that supports the load for 1/4 - 1/2 second until the alternator responds.
There is no point trying to boost the voltage. The amplifier is designed to work with a 9 - 16 V input and it has it's own boost circuit to give a higher voltage to the speaker.
Anywhere near full power with an amplifier like that will be deafening. A loud bass beat will take a lot of power, but not for long, and the battery will support that, as the load will come on and go off too fast for the alternator to respond.
Unless you want to run demos all the time, the standard alternator and battery will most likely be fine. If not, the battery will be discharged and you will have to turn off the music until it recovers.
As Gophert said, you can't do anything about the power the alternator produces. If you want more, you need a larger power of alternator. That is why alternator upgrades are used. If there was a swift cheap solution, it would be used.