Great news! That's totally possible!
When you create your Widget, you can, if you'd like, mix and match "Automated Codes" (codes that Tada generates for you within your Shopify store) and what we call "Existing Codes" (those are the custom codes that you create yourself in your Shopify discount section.
Please note that Shopify itself only allows for one discount to be applied at checkout, which means that none of your visitors will be able to use two discounts, whether they're coming from Tada or not, during the same checkout session.
What are the discounts that I can apply?
Is it possible to have both Automated and Existing codes?