I've been out of the car audio game for a while (since late 90s), but I know cars and electronics--wouldn't adding more batteries be counter productive to creating higher wattage while the engine is on? More batteries means a bigger load on the alternator which means less power when the car is running. More batteries, on the other hand, would create more power when car is off.
To get more power with the engine running you'd need a bigger alternator.
Either way, id say run it and see how it works before investing in anything else. Lights dimming isn't much of an issue in my opinion. My lights have dimmed for 15 years and my battery has only dies at the drive in once. Granted I've never ran over 500w rms, but my car also only has an 80amp alternator.