We’re currently using the Shopify Menu which has a limit of three tiers (1 main, 2 heading, 3 sub-heading). However we’d like to add a 4th tier. Does anyone know how we can add this?
Hi @melanies23 
Why make customers dig that much through menus.
When a sites navigation gets that complex that indicates bad choices have been made in structing the sites navigation.
When you reach the normal limits of a system you need to either customize the theme or use apps.
To DIY a solution research the net or forums to figure how to do something like tie one menu to another menus children etc.
If you need this customization and have a strong use case and budget then contact me for services.
Contact info in forum signature below 
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ALWAYS please provide context, examples: store url, theme name, post url(s) , or any further detail in ALL correspondence.
Hi @melanies23 ,
This is possible, you need to change the menu display code for it.
So for 4th menu, you will need to create a separate menu and use a handle to be able to display it in the 3rd menu. Refer code:
{% for link in linklists[menu_handle].links %}
{% endfor %}