A group of Microsoft Products and technologies used for sharing and managing content, knowledge, and applications.
Hi Jonathan,
From the graph you posted, you are using the Structural Navigation. Please try the Managed Navigation via the steps in the article first.
Then click Site Settings>Look and Feel>Master page>check what master page the Home page is using>Open SharePoint Designer 2013>find the master page>change MaximumDynamicDisplayLevels="2" and MaximumDynamicDisplayLevels="0" to MaximumDynamicDisplayLevels="4" to see the outcome.
If the issue persists, as the requirement can’t be fully achievable by the out-of-the-box feature, I suggest you post a new thread on our TechNet forum to see if there is a customization way to do that in your environment.
Thanks,
Cliff