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Hi @Michael Philipsz ,
It seems this is not a common issue per my test. However, we can work together to narrow down and resolve the situation.
1.Assign Full Control permission directly to the affected user account.
2.Clear the cache of the SharePoint Designer.
3.Open SharePoint Designer and connect to the site collection again, when it’s prompting to input the login account, make sure the Keep me signed in is checked.
If you've tried all of the above methods, you can also check out the methods in this document and let me know if they work: https://answers.microsoft.com/en-us/msoffice/forum/all/sharepoint-designer-2013-server-error-access/63a3358c-3722-49b6-a15e-e7a1dfa2e3c1
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