This is an accepted solution.
Elias here with Shopify Support. Thanks for reaching out.
Currently Shopify doesn’t support stacking discounts, which includes automatic discounts as Customers will be cancelling the automatic discount in order to enter a different discount code. One workaround is by setting up shipping profiles and offering free shipping for certain products. However, this will only work with free shipping as the combined checkout rates is designed for products with drastically different shipping rates as the rest of your products (eg. Fragile products).
Alternatively, if shipping profiles doesn’t work for you, you can stack discounts by using third-party apps. I’ve handpicked a couple for you to try out:
If you require assistance with these apps, you can always reach out to the developers directly through the contact information found in the Support section of the app’s page.
I hope this provides some options for you to explore. If you have any more questions regarding discounts, feel free to reply to this thread and I’d be happy to help.