The backend version is not supported to design database diagrams or tables
I ran into this problem when SQL Server 2014 standard was installed on a server where SQL Server Express was also installed. I had opened SSMS from a desktop shortcut, not realizing right away that it was SSMS for SQL Server Express, not for 2014. SSMS for Express returned the error, but SQL Server 2014 did not.
This is commonly reported as an error due to using the wrong version of SSMS(Sql Server Management Studio). Use the version designed for your database version. You can use the command select @@version
to check which version of sql server you are actually using. This version is reported in a way that is easier to interpret than that shown in the Help About in SSMS.
Using a newer version of SSMS than your database is generally error-free, i.e. backward compatible.