This isn't likely to be achievable through CSS alone. There is a really, really obscure hack which involves using hidden checkboxes and CSS sibling selectors, but what you're asking for here is a link click to open a menu of sorts. It sounds like you're going to need to use Javascript to accomplish this. Depending on what sort of menu you're after (whether it's a dropdown or a flyout) you'll need to have a search online to find one that suits your needs.
Bootstrap offers dropdown/menu support out of the box (
Navbar · Bootstrap[
^]) if you're open to using it, otherwise you'll have to use Google to find what you need!