I have three computers in a wifi network. I have a Time Machine disk attached to one of these and would like to back up all three computers to the same disk. I have tried to share the Time Machine disk to make it available for the other computers but get an error that I don't have the privileges to write to that disk.
How can this be solved?
Mac mini, macOS 14.4
You need to create another APFS Volume on the drive and share that out for the network users.
A direct-connected drive is fully owned by Time Machine and cannot be altered. If you create another Volume, the only volume Time Machine will own for that computer is the volume you assigned to Time Machine on the direct-connected Mac.
You can assign a quota to the direct connected Volume. The network backups will create sparse bundle disk images in the second Volume and will share all of that space. You could create a separate volume for each network Mac and set a quota if that is desired. Give each at least twice the size of the drive you are backing up. In order to set a Quota for the first Volume, you may have to start over by erasing the drive, then create the volumes. Changes have been made that I think allow that, but I don't have an external drive with me to play around with.
Add, delete, or erase APFS volumes in Disk Utility on Mac - Apple Support
Backup several computers with Time Machine to a single shared drive
