Dear Lawrence,
Welcome to Microsoft Q&A community!
Firstly you could check the following official document to remove the accounts for New Outlook:
Add an email account to Outlook for Windows - Microsoft Support
There is no mention of needing to remove other email accounts first when trying to remove an account in the new Outlook for Windows.
If the issue persists, please let me know the followings:
- What’s the type of these three accounts?
- Please provide the screenshot for the error message.
If anything is unclear, please feel free to let me know.