Depending on the configuration of a SQL Server, available threads can be used if you create a snapshot backup of many databases at the same time. Microsoft has an article referring to the issue and it's workaround:
- If you are running a 64-bit version of SQL Server, you can consider increasing the Max Worker Threads configuration option.
- If you are running a 32-bit version of SQL Server, please check the influence of increasing of Max Worker Threads to performance.
How to configure the Maximum Number of Worker Threads (SQL Server Management Studio):