To apply twice the voltage to a speaker, a convenient method is by bridging it between two amplifiers. Each amplifier has the same positive supply. The load gets true AC.
Another option is to install a buckboost converter. It inverts supply polarity, and is ground referenced, thus you can continue to use the chassis as 0V ground. If you wish you can use a boost converter to raise +12V to 24V, etc.
Another option is to create a +12-12 split supply, by pulsing 2 stacked capacitors (possibly add an inductor, buck converter style). This method isn't ground referenced, so you might decide it's inconvenient.