This feature is not yet available to all Shopify Stores.

For those merchants with early access to this feature, customers can apply multiple discount codes to the same orders. To ensure this can be done, you must make sure that you edit your individual Discounts in the Shopify Admin so that they can be combined.

For those with access to this feature, Shopify has made it very easy to do this using the Combinations section of the discount creation.

In this example, we’ve edited one of our Free Shipping Discounts so that it can be combined with both products as well as order discounts.

In turn, we’ve also made sure to edit our products and orders discounts so that they too can be combined with the Shipping discounts and used together for the same order.

For more information on combining discounts please check out the official Shopify article discussing this new feature.