Hope this helps someone. I was stuck for a while trying to figure this out.
We have a product where customers leave shopify and land on a remote site. They customize their product on the remote site and then return to Shopify to continue shopping. We wanted to have a [Add to Cart] button on the remote site that would add the item along with the customized data to the cart of our shopify store.
Permalinks didn't work -- couldn't add the custom data to the line item, only the cart.
Storefront API didn't work -- couldn't add item to the shopify cart already in user's session.