Navigation Level Limits

Your theme is able to create nested menus up to 3 levels deep - the Shopify admin area's limit - from a single page by using the menu editing interface.

Here is more information on how to do this: Shopify Help - Drop-down Menus

There is also the option of using the mega menu feature which increases your layout options. More information is available on this towards the bottom of this page, along with a useful tutorial video:

Apps:

You also have the option of adding additional functionality, via the use of an app, to display additional layers of navigation such as:

Globo Mega Menu - Shopify apps Buddha Mega Menu - Shopify apps Meteor Mega Menus - Shopify apps