Private app limit - Add additional section to the checkout page

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Hi Shopify Community!

I would like to create a Shopify app that adds an additional section to the checkout page. 

--> A possibility to contribute when the user chooses to check the contribution checkout (displayed in our additional section) ... the value of the contribution will be added to the total amount to pay.

** First, I've started to develop a public app, but it seems forbidden to modify the shipping page neither through a scriptTag/proxy app nor through the StoreFront API.

My question here is: is it possible to apply my app idea using a private app ?? 

You find below an image of how it would be if it's possible (Sections to add are borded with red).

I would appreciate any advice.