By default, the theme is using 3-level dropdown menu. Also, there's a Mega Menu functionality which can be used instead of a standard dropdown.
Here are the steps to setup a Mega Menu for your needs:
1. Create Main Menu in Shopify Admin > Online Store > Navigation. For the mega menu, you only need to create top-level menu items. Example:
2. Set the menu that you've just created to be the main menu. Open Theme Editor (Shopify Admin > Themes > Customise), select 'Header' section and select the main menu.
3. Click on ' Enable Mega Menu' checkbox to enable mega menu functionality.
4. Now, you need to add Mega Menu widgets. Click ' Add content' in the bottom of Header section. There're a huge amount of widgets to choose from.
5. Important! For each widget, make sure you specify the menu item it belongs to. For instance, if we want to add categories navigation as a mega dropdown to 'Catalog' menu item (as on the example above). Click 'Add Content' > Menu, select the menu you want to display and specify Menu Item field with 'Catalog' or '1' (because it's the first item in the menu).
6. The same way you can set all the other widgets you need to use. The widgets approach is really intuitive and gives you an ability to include any content you want.