Hi Bigcatbooks,
It is possible to do what you have in mind however, there's a bit of programming involved. Check out this info. Another option is to build a Square website for online sales and link that site to yours. No need to transfer domain names. In the past we did this, we just added a link on our site for shopping - it takes the customer to your Square site whereas they can select items, use the cart and checkout.
jk
