File Permissions and Time Machine

I want to know if there is a way to set file permissions on Time Machine Backups (Encrypted .sparsebundle Files) to prevent accidental deletion by family members or others while sharing the storage device that the backups reside on while still allowing all backups to continue. Specifically the Time Machine Backups should be able to be deleted by one person only. What do I need to do to accomplish this without interrupting the Time Machine Backups from the three computers that backup to said storage device?