Is it possible to change the drive that Microsoft DPM backs up to?
DPM and Windows Server Backup make a determination when the agent is installed as to which drive it would use for System State Backups. 

This by default is the drive with the most available free space. That information gets saved into the PSDataSourceConfig.XML file.

WARNING:
If the server you are protecting is a member of a cluster, it is possible that a cluster drive will be selected in this process. If that drive ownership has been switched to another node, then next time system state for the node is done, the drive is no longer available and the backup will fail. In this situation, you will need to modify the PSDataSourceConfig.XML to point it to a local drive.


On the server you are backing up, navigate to C:\Program Files\Microsoft Data Protection Manager\DPM\Datasources.
There you will find a file named PSDataSourceConfig.XML. Right click that file and choose to edit.
Find the section for  which is followed by a drive letter and WindowsImageBackup. This will be the current location WSB will put the files.
Modify the file to reflect the drive letter you want WSB to use.