At this point, let's assume shareholders are educated and on board. Let's also assume you have a clear set of browsers that you would like to add enhanced experiences for. We can now set about tiering the experience. I like to keep things simple, so where possible I opt to define a simple 'base' tier and a more 'enhanced' tier.
The base experience being the minimal viable version of the site and the enhanced version being the most fully-featured and aesthetically pleasing version. You might need to accommodate more granularity in your tiers, for example, forking the experience in relation to browser features; support for Flexbox or support for translate3d for example. Regardless of how the tiers are defined, ensure you define them and what you expect to deliver with each. Then you can actually go about coding those tiers.
Right now, Modernizr facilitates the most robust manner to enhance and fork experiences based upon device capabilities. While it means adding a JavaScript dependency to your project, I think it is worthwhile.
Remember, that when writing CSS, the code outside of media queries and without selectors that require classes added by Modernizr should make up our 'base' experience.
Then thanks to Modernizr, we can layer on ever more enhanced experiences based upon the browser capabilities. If you refer back to example_08-07 you can see this mind-set and code pattern applied to an off-canvas menu pattern.