You can configure dbccdb to run dbcc checkstorage concurrently on multiple databases.
However, this is possible only when the second and subsequent dbcc checkstorage operations have their own dedicated resources. To perform concurrent dbcc checkstorage operations, each operation must have its own scan and text workspaces, worker processes, and reserved cache.
The total space requirement for workspaces depends on whether user databases are checked serially or concurrently. If you run dbcc checkstorage operations serially, the largest scan and text workspaces can be used for all user databases. If you run dbcc checkstorage operations concurrently, set dbccdb to accommodate the largest workspaces that will be used concurrently. Determine the workspace sizes by adding the sizes of the largest databases that will be checked concurrently.
See the Reference Manual: Tables.