I was reading some posts, your lights don't dim because your alt cant keep up with voltage LOL HA HA.. Your alt puts out a constant Voltage LOL! What it cant keep up with is the amperage with in it puts it out the voltage... thats why a cap will show a drop in voltage ONLY because your amperage drops, so it sees less volts coming from the alt.. there is a big difference..
First do the big 3, while doing that but a nice battery under the hood..
Now.. heres the key part.. adding a second battery will infact do you no good as your alt wont be able to keep up, but what you can use is a CAPCELL, its a fusion of CAP in terms of the way it recharges quickly and discharges quickly, but holds amperage and volts as a battery would. It is essentially a battery but designed like a cap.. Fast discharge/recharge...
So with that said, you can infact add a Capcell to suppliment your amperage that your alt is lacking, but you cant go crazy.. a 800 series capcell will discharge 800 amps in an 8 second period.. so that means once the 800 amps are used up they are gone if your alt cant recharge it quick enough, and chances are it wont be able too, it will drain your battery of what amps it has.. so your not gonna be able to go crazy adding a bunch of extra amps..
what you can do is, here are the specs.. 800 W/Rms will consume around 80 amps (depending on the class of the amp and the design) but norm is 10amps for every 100 w of power.. so if you do the math, if you charge up a 800amp capcell it will supply the amps you need to run your system, at a rate of aprox 80amps/sec for 10 sec's
So with all that stuff said above, as far as the numbers go, listening to music you should be able to run with no dimming lights for the most part.. your alt should be able to keep up the charge as the Main battery and Capcell will discharge during musical peaks..
You may have dim during extendended musical peaks, or while listening to hardcore bass sweeps, but for most everyday driver type music you should be ok.. just remember dont go overboard with it.. The battery and Capcell can only will recharge inbetween musical peaks.. depending on teh type of music you listen too..