Can I have two separate Time Machines and exclude the macOS on one?

Technically, Time Machine already does not backup the volume containing the macOS proper. TM only backs up the "... - Data" volume that contains your Home folder and user files. This behavior since Big Sur, I believe.

TM doesn't like to share drives and it definitely won't share volumes with other apps.

It is also not advised to use a single drive with multiple partitions to home both TM backups and other data. That is simply asking for trouble as you would potentially lose both when the drive fails.

While you can use TM to backup a Mac OS Extended (Journaled) formatted external drive to another, it would be an inelegant solution and would have to be manually assisted. One cannot define multiple back up setups for TM, i.e. TM cannot be set up to automatically exclude some data from the backup to one drive and use different exclusions for the backup to the another drive.

You don't say what the "other software" is that you are trying to use for backup, but I would strongly suggest you look at Carbon Copy Cloner from bombich. That app is most reliable, most flexible. extremely capable and can accomplish for you exactly what you are trying to do.

Yes, you can use two Time Machine backups.

You cannot exclude the macOS system volume only, but you can exclude all internal folders so the second backup effectively contains only your external hard drive. Time Machine supports backing up external drives as long as they’re formatted for macOS.

I mean exclude.

You want to exclude the OS files on your Mac from being backed up in one TM backup. Easy to do because TM does this automatically anyway.

You want to exclude the user files on your Mac from being backed up when the second partition is getting backed up to the second ext drive.

TM cannot be configured to do these two separate backup tasks. TM is designed to backup your user files, accounting for exclusions, to a single ext drive or to multiple ext drives. But the exclusions don't change.

CCC can do all of this, and on a schedule.

You cannot create a second backup definition for Time Machine.

You can do that with CCC or with another backup app such as SuperDuper! from shirt-pocket software.

What you mean by macOS??

Currently system and data files are separated to different APFS system and data volumes.

By default 3rd party backup utilities like Carbon Copy Cloner backup only the data volume and AFAIK Time Machine behaves about the same. Optionally also System volume can be backupped with CCC. But only with the initial 1st backup and not so easily in M series Macs.

So user data files can be backupped but sometimes they might not be compatible with old macOS system. Photos library is an example -- if a newer macOS has touched it, then it is automatically updated and incompatible with the older macOS.

Cindy-G5 iMac__ wrote:

I want a second Time Machine to back up an external HD to another.

CCC can backup desired folders.

BUT if I want to backup certain bootable Intel macOS, then I prefer to boot to that macOS and then use compatible CCC for THAT macOS to backup it as bootable volume or "bootable" .dmg image that can be then cloned to a real bootable volume.

A while back I tested this. For the record I noticed the following requirements:

macOS_10.14.6 bootable .dmg must be cloned with CCC 5 when booted to macOS 10.14.

macOS_10.15 bootable .dmg must be cloned with CCC 6 when booted to macOS 10.15.

macOS 11-15 bootable .dmg can be cloned with CCC 7 when booted to macOS 15.

Cindy-G5 iMac__ wrote:

Do you mean include? I’m talking about the files on my MacBook.

Yes, I meant "include". Time Machine does not backup the macOS System files.

It only backups your own files and data. So not sure what you are trying to exclude then.

As mentioned its not recommended to share the Time Machine drive with other apps or files as that a lead to data corruption.

Time Machine backups do not incluce macOS system files.

Back up your files with Time Machine on Mac - Apple Support