Tips and considerations for embedding story maps
Here's a couple of posts that cover considerations and tips for embedding story maps in websites, and also embedding story maps in other story maps.
Tips for embedding story maps in websites | ArcGIS Blog
Embedding a Story Map within a Story Map | ArcGIS Blog
A good example of embedding a story map in a website is this one about where the jobs are (and aren't) from Forbes:
It uses Story Map Series with the side accordion layout option, and takes advantage of the &embed URL parameter discussed in the first post.
The example below embeds another story map - a Story Map Swipe - inside a Story Map Series (tabbed layout) on the third tab.
When embedding story maps inside of story maps, less is often more. Embedding story maps within a story map can complicate your story by providing to many paths to follow, and too much media to look at. The best story is often the simplest, pared down to its essentials. But used sparingly, embedding story maps in story maps can be effective an useful technique.