Today, I will explain you How to fix the server could not complete your request SharePoint 2013. When I tried opening SharePoint 2013 site in SharePoint Designer, I got the following error:

When I clicked on Details, it opened another dialog and continuously pop up window is opening and not able to open the SharePoint site.

And here is the error message:

Solution:
1. Go to Run -> then  type Inetmgr -> Now Open the IIS
2. In the Web Sites select “SharePoint Web Services” in the list as you can see on the following picture

3. Next step, click on the Authentication and Enable “Anonymous Authentication” as shown on the below picture:

4. After enabling this, I am able to open the SharePoint site in designer without any issues.

Source : sharepoint2010europeanhosting