Shopify plus store, customize checkout discount handling

[Wieknot]

First, we do have our checkout.liquid file unlocked so that we can customize our checkout.

We have a 3rd party app that allows us to have multiple discounts per order, a feature that is surprisingly not built-in by default. This 3rd party app doesn't quite do everything we need, so we are researching if we want to make a custom app to handle our discount-related needs.

I have a pretty good handle on how to edit what is displayed in the checkout process, but I'm struggling to find how to edit line item prices and or attach discounts to multiple line items, so the order that gets created reflects these changes.

Can anyone point me to one or more articles/docs that could help my efforts?