I think the answer to this is ‘you can’t do that’ but I’ll ask anyway.
I have a Mac Mini on my home network with a networked Time Machine volume. Other Macs on the network back up to it without incident. However, when I try to add the networked drive as a backup destination on the Mac Mini itself, Sequoia wants to reformat it. I remember trying this back in Catalina with the same results.
Yep, definitely don’t do that. You can’t stick sparsebundle images of other machine backups on the same volume as your own TM backups.
Instead, use the magic of APFS to create a new volume, which is a non-destructive and space-efficient process, then tell TM to target that instead. You probably also want to make sure that your sharing settings limit the maximum size of each machine’s backups, or else set quotas on your new APFS volumes, such that either the local backups or the remote backups do not grow infinitely and completely exhaust the disk, but that’s strictly optional.
This works and is how I rolled for some time. But nowadays I’d only consider this for purely wireless, portable use of Time Machine, and given the problems that network Time Machine backups seem to introduce, eventually, with corruption of the sparse disk image filesystem, I’d suggest using Arq, instead. Arq isn’t as comprehensive but it’s surely more robust. Or maybe networked CCC, if you don’t mind using the legacy copier (and therefore having no snapshots support).
If a user already has a CarbonCopyCloner license…creating a share on the destination Mac and using the Remote Macintosh destination selection rather than the volume destination is easier and cheaper…and it makes Finder readable copies, does versioning like Time Machine…and actually works where as TM to a remote destination is severely problematic and fails a lot in new and unusual ways that despite being a Mac guy and consultant since the late 80s I scratched my head over until I just rolled my own TM like solution with CCC. And unlike TN you can configure it for whatever intervals you like including alternating between destinations by setting up 2 tasks with the correct scheduling applied.
TM works just fine for local drives but not reliably over the network. I did plug in an old spinning drive to the laptops and set it up as TM destination but it never gets plugged in again…but having TM on makes the local backups on the SSD for quick recovery if an inadvertently dumped file.