Is Shopify able to read information from a remote script for shipping?

[MicaCharise]

We want to apply an $8 markdown on the FedEx rate on our shipping costs on checkout. If the FedEx rate is cheaper than $8 the customer would receive free shipping, otherwise they would pay FedEx to charge less $8.

We found an app https://apps.shopify.com/intuitive-shipping that could do this logic. However, we want to avoid the monthly app costs if we can do the tech ourselves.

Is Shopify able to read information from a remote script? We were thinking we could perhaps write our own PHP script on our network that could feed the shipping price to Shopify. Would it be possible?