Overcharging alternator?

I have a 2001 honda accord with a 2.3L engine. The alternator is rated at 80 amps. I recently put in a top of the line stereo system with two amplifiers each drawing 40 amps peak. Using only one amp, everything runs fine and sounds ok. As soon as I turn on my subs (using the other amp) the lights dim, and the sound distorts terribly. I know this is because my amplifiers are drawing more power than my alternator can provide, so everything drops. I currently have a capacitor installed, so thats helping the load. I looked into rebuilding the alternator, and I know that that would help, but what else can I do? Would adding more capacitors or batteries lessen the workload on the alternator? Again, I only have the problem when the bass hits are strong, so its not a constant strain.