I can tell you what I would do after I tell you what I have already done myself.
I have a Civic with a stock alt (70A) and an HC1400 under the hood. I run about 950W RMS between my 4ch and mono sub amps. I have the Big 3 done and 2 gauge wire ran for both power and ground to the rear. I have zero dimming even at idle. My voltage at my amps never dips below 12.8v, which is pretty good on the stock alt.
Now you are looking to run more audio than I have, so what I would recommend for you is a little more. The first thing you need to do is the Big 3. It is for sure necessary. Second is to run dedicated power and ground wires to the trunk where the amps will be. I would suggest 1/0 gauge wire in case you need to add another battery in the rear and it will give you better voltages in the back due to less resistance. Third step is to replace the stock battery with an AGM style battery. The bigger the better. Buy the biggest that fits in the stock location. I see in previous posts that you own a 2005 Grand Prix. The stock battery is a G34 IIRC. That would be a D3400 in the PowerMaster line. Those steps should get you started, but I doubt it will be enough.
Now that you have the basics done, now you can test out the setup and see where your voltage is at. You will want to test the voltage at the amps power inputs. If you are seeing a drop to below 13.0v at the amps, I would now suggest getting an additional matching D3400 to add in the trunk. Buying matching batteries will make them last longer. You can ignore this advice if longevity of the battery is not a concern and buy a bigger unit, like the D3100.
With the second battery installed, if you are still seeing significant voltage drops, it is likely due to the batteries not maintaining a full charge. At this point you will need to replace the alt with a HO alt. This would be the last step and would most surely be the last step.
M GO BLUE! //content.invisioncic.com/y282845/emoticons/veryhappy.gif.fec4fed33b4a1279cf10bdd45a039dae.gif