Unfortunately, folks have been trying to get Shopify to add some functionality on shipping options for a long time...and they seem unwilling or unable to provide for more than one dimensional weight option. You can see this post with a year's worth of requests.
If you have flat rates for delivery and installation, though, you could set them up as product variants, rather than using the shipping. You would set this up with each product. For example, you could create your product for piece of furniture for $500. Then you could create a product variant (option) that includes delivery for $575, and a second variant that includes delivery and installation for $650.
You'd definitely have to get an app for anything more difficult like calculating distance from the warehouse or variable delivery/installation options.