[Some wonky audio from the app. Not throughout. With our apologies nonetheless.] What can't go over the schach: for example, additional shading, such as a tarp or a canopy. Any such thing that can be rendered impure cannot be kosher for schach. But if you are intentionally beautifying the sukkah with decorations, that should be fine. The discussion of roofing that can be rendered impure does get some attention here, but as a given. Also, an exilarch (resh galuta) story, with a sukkah and schach that was hanging down. And it was treated as not problematic davka. Plus, the case of a bed with netting over it. And the case of sleeping under one's bed in a sukkah.