I am opening another e-commerce site that will sell different products. Can I use the same account and set up the second site as another location? Or do I have to set up a separate Square account for essentially a different business?
You can do either or. But if both e-commerce business are selling different products, your best bet would be to set up a new account to keep sales, reports etc separate. Here is some more info on it in this thread.
Ultimately it is up to you on which way you prefer.
