Nick here from Shopify. Great question!
That shouldn't be a problem at all. You can set up as many different stores as you want with one SSN number, each store can only have one SSN number though. Something to remember and be aware of with multiple sources of income (multiple stores) coming through to one tax ID is to make sure all your taxes are in order. Let me know if you have any other questions about this or anything else.
All the best, Nick