I’ve been asked to handle a structural edit (SE) often enough, but I’ve never had the sense that the house that is asking for one actually knows what it wants, except that it’s more than a CE. You’ll find plenty of definitions of a structural edit online, all saying roughly the same thing, but remember that every mscript is different, which means that when it needs an SE, it will be a unique SE, the same way that every CE is unique in its own way. Mscripts are like cars that way – they all run on basically the same principles, but every breakdown or dent is going to be a little or a lot different from the last one you faced.
A CE always involves structural work at some level. When you hire a proofreader to copy edit a mscript, the result that’s returned to the house will mostly likely resemble a proofread. When you hire a copy editor to handle an SE, you’re going to get a CE with some blocks of text moved around (or deleted) in a useful way. That’s how I always approached them – as a super-extensive CE.
Whatever instructions come with a request for a structural edit, best if you ignore them. You’re going to be digging into the mscript deeper than anyone but the author, and you will be catching things that even a close reader would not have caught.
There isn’t much to an SE that an experienced copy editor doesn’t already do as a matter of course. The “structural” work is simply CE work at a higher level. The task is still about smoothing the reader’s way, but you’re working at the level of paragraphs and sections, or even entire chapters, in addition to the sentence level. I’m primarily a copy editor, so when asked for an SE, I always start at the sentence level while keeping an eye out for sentence placement. You parse each sentence, then check the paragraph for internal flow, then consider whether the paragraph is in the right place and move it up or down (or delete it) to the degree it makes sense to do that. And the same with chapter sections – shuffle them around if you think it will help, and then double-check that the sections still flow smoothly, one after the next. When you hire a CE to do an SE, that’s what you tend to get, and it’s as good an approach as any, because more thorough.