Clean & tighten ALL battery connections, grounds, starter & solenoid positive connections & see what that does. You have a bad connection or corrosion somewhere.
I've run as much as 2200 watts, 4 subs, 6 midrange & tweets off a stock GM alternator & 1000 amp battery & never had issues. If your lights dim with heavy bass thumps try a 1/2 Farad cap wired to the amp.