Please, note that Filter Menu is not a hierarchical menu system. It is a faceted search system, so all filters sit at the top level. Meaning also you can't have sub-categories, and sub-sub-categories nested under one top-level filter right away.
However, there are great options to navigate your customers down to each sub-level.
To achieve this you need to create filter groups for all levels, for example, for continents, countries, cities, and so on.
Then we can use Visibility options, in this scenario once we have filters created for all categories (Europe), subcategories (UK), and sub-subcategories (London) we can let customers be able to search through and set visibility option in a way that subcategories and sub-subcategories will only appear when one of the parent filters is selected.
They select Europe, then the filter with countries (UK, etc) appears, they select it and the filter with cities appears.
In this case, we will still be able to allow customers to filter and the matching search results based on filtering through all the collections you have if needed for particular filters (as searching particular size through all the locations).
Here is a guide on visibility options:
By default, selected filters will override the visibility settings, this is done to show your customers that a filter is selected. If you do not want this behavior you can disable the setting for "Active filters override visibility settings" - this will stop the selected filter from showing on the page where the visibility settings are set to hide that filter group.
You can find your theme settings for the Filter Menu by going to 'Online store' in your Shopify admin, then click 'Customize' next to your theme name, then click on the "Theme Settings" tab at the bottom of the sidebar, select "Filter Menu" and scroll right to the bottom to find the Advanced options.
If you have any additional questions, please contact support through the live chat in the app, or at firstname.lastname@example.org