Discount Mixer is a Shopify application available from the Shopify app store. It works with Shopify discounts and supports enhanced features such as stacking and the maximum amount that Shopify discounts don't have.
Once installed, it adds a widget to the Cart page, where your customers enter their coupon codes. Automatic discounts apply automatically. The discounts are carried over to the Checkout page once the customer clicks the Checkout button.
Apply Discount on Cart page
Discount carries over to Checkout automatically
Applying discounts in action