Partial Discount on Shipping

We need a solution where a product is "free" for shipping unless someone chooses priority shipping. So, if regular shipping would be $10 but the person wants it faster than 3-5 days and wants to pay $20 for shipping. How can we charge the person $10 for the shipping? So it's "free" (with a catch).

You can do that with current Shipping Method -> Manual (Fixed or By Weight)
http://yourwebsite.com/Admin/Shipping/ConfigureProvider?systemName=Shipping.FixedOrByWeight
Dont tick Free Shipping on Product
Use Admin -> Configuration -> Shipping to configure Shipping Method
You can provide options
Free Shipping ($0.00)
Fast 3-5 Days ($10.00)
Very Fast 1-2 Days ($20.00)

ntbuddy wrote:
Note that shipping is for the entire cart.  If you have specific product requirements, then it there are other considerations.