Caps can be a huge hinder on systems because of the discharge rate, basically they have no reserve and makes your alt work harder to try and recharge them, so at full tilt a cap is worthless. With 3 batteries (believe is what you said) you should have no issues at all. Something is wrong with the way it is set up.
Somebody needs to brush up on their electrical theory....
Caps will NOT "hinder" a charging system. Why would you say that they make your alt work harder? Caps are nothing but a small storage device...LIKE A BATTERY!!!! The difference is that caps release their energy far faster than a battery....WHEN IT IS CALLED FOR! Music is dynamic. Large bass transients need LOTS of power NOW! So, it's not so much "how much" energy you are getting to the amps, it's WHEN you are getting that energy to the amps.
The big myth about charging systems is that more batteries will help stop dimming headlights. Ummm...sorry, it's the other way around. A battery is a LOAD! just like a light bulb. It takes approximately 10 amps of your alt to MAINTAIN a full charge on the average car battery. So, the more batteries you add, the more of a drain they are on the charging system! In effect, you have added an additional 20 amp load on the charging system, by adding two more batteries. And, made your lights that dim at full tilt, music output...dim more than ever! Remember, batteries are not a SOURCE of energy, they are storage devices for energy created by the alternator. YES, they are a storage device. A storage device that holds lots of energy, but due to it's internal resistance, it discharges SLOWER than a cap. A cap is also an energy storage device. But, due to it's smaller reserve, it takes
LESS energy to bring it back to full charge. Unlike a discharged battery that might take hours to return to full charge.
Now, the interesting part here, is that a cap should be the electolytic canister type. NOT the carbon type, that resemble a battery. The large, 100 Farad type caps ARE useless. Because, they share the same problem as the battery....high internal resistance. The cylindrical, canister, electrolytic type caps...with LOW internal resistance, are what will help your charging system. BUT, you will need 1 farad of capacitance/1000W of amp power.
To respond to the OP...
Now, caps will only help you get over SLIGHT dimming. In your case, you are relying on battery power to play your system, with the ignition off. You will benefit from more batteries, for THAT purpose. BUT, you will most likely need a larger alt to keep THEM charged.
I have 2900 Watts in my system. I will only get about 15-30 minutes of play at moderate listeming levels. I have one battery. With two, I might be able to double that time. OR, I can just listen to the system with the engine running.
I would definately spring for the larger alt. And, I would get an AGM type battery if you don't already have one. They can discharge deeper, without damage. They can recover again, and again. And, they still can be used as a starting battery.