Yes we can. We are Shopify partners. This means that we can fully integrate your site with a Shopify account and cart.
If you already have an account with another e-commerce provider, we can work with them too. All we need is a snippet of code exported from their platform. We can easily embed it into any of our blocks.
If you would like to offer gift certificates, we recommend creating a landing page with a button to a Stripe or PayPal product page.
Those sites are trusted and can handle the money for you. Here's an example of a client doing just that: https://www.amarillochiropractor.com/pages/gift-card