You approach makes no sense. You should not keep convincing yourself that you problem is CSS. You problem is structure. Multi-level menu is described in enormous number of places, for example,
http://www.cssscript.com/create-a-multi-level-drop-down-menu-with-pure-css.
Your HTML is not multi-level, period. There is nothing to work at. The example shown above demonstrate humane approach, as well as many other.
—SA