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Hi and thank you for your question.I want to make sure I understand. You have a stereo system that is being driven by a 600 watt amp? If that is correct, you are definitely going to need at least one more battery and depending on how long you want to run the stereo, you may even need a 3rd.
Another alternative is to use a deep cycle battery just to run the stereo. If I have calculated and interpreted what you told me correctly, the largest deep cycle battery that Interstate makes would power your stereo for about 3 hrs. That particular battery weighs 117 pounds and has a suggested retail price of $240.
Let me know if you have any more questions or if I am misunderstanding what you are asking.