Should I add my new e-store to my existing website or build a whole new one?
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Unless you have a really good reason to use a new domain, you should use your existing one. It already has some age and content. That will really help you to rank higher in the search engines.
You current website probably has some traffic too, so I don't see why you would want to start from scratch when you already have an asset that you've been working on for so long.
Best of luck with your new e-store!