Time Machine to remote external HDD

From Big Sur, Time Machine will take control of the drive and not let anything else onto it. You would need to partition the drive in Disk Utility. One part for the iMac Time Machine, and another part for the other network backups. They can be on the same partition as Time Machine will create a separate disk image for each.

When you share out that partition, Ctrl-click on it in Sharing and choose Advanced options to set it as a Time Machine backup.

I create a single Sharing Only user for Time Machine and use that to connect to my Mini hosting the network backup drive.

What is the format of the external drive? My guess is that the format is not compatible with Time Machine.

Now if you attach an external disk and use it as a Time Machine backup it gets formatted and made Read Only (except for Time Machine).

You might be able to use an external drive on another Mac if that drive has a dedicated partition for Time Machine. You might need a partition for each Mac.

nsss1970 wrote:

By the way, I have created a new APFS volume, not a partition.

It seems that way the whole physical disk space is available for all volumes, according to the space they need.

(With a partition, it seemed I needed to pre-decide how much space I allocated to each partition)

If that works, great. I tried creating a new (local) TM backup on a Volume and I thought it didn't work that way, but maybe I'm confusing it with something else. Or, they have since fixed it.