Hi Ben,
Well, if you mean reaturning the page contents as individual results (page parts as results), then that is unfortunately not possible, as those are stored as a single page within the WordPress database.
If you mean searching the page contents and returning the corresponding page, for example contents that are printed via shortcodes and not immediately present as text in the database, that might be possible, via using the Index Table engine. If you follow the steps within those documentations, it should do the trick.
You can make minor changes to the results templates, via results templating. That way you can add additional classes, other attributes, as well as elements if needed.