Move Time Machine Backup macOS Tahoe

You cannot move or merge TM backups. In theory, assuming that by ‘Airport Time Machine’ you mean Apple’s Time Capsule you can remove the hard drive (which is no larger than 3 TB) from it and place it in another enclosure.

To continue backing up your Mac(s) over WiFi with macOS 27 and later (Time Capsule works with Tahoe), the most straightforward way is to use a network attached storage (NAS) device – essentially a box for hard disks that connects to your network. Ideally, choose one that offers turnkey support for Time Machine out of the box, both Synology (setup instructions) and QNAP (setup instructions) do so.Technically, you can stand up a Time Machine server in other ways (including using a Mac as a TM server), but an NAS is arguably the most straightforward way to set up network Time Machine backups. 

Personally, I use a Synology DS223j with a pair of 10 TB HDDs installed to back up 5 Macs in the house with Time Machine (separate shared folder for each Mac sized at ~2.5x the internal storage), with the remaining space used as general file storage for everyone in the house.

The Synology manual says:

1. Starting from macOS Tahoe 26, Mac File Service (AFP) on SRM only supports existing Time Machine backups. As macOS 26 does not support creating new backups via AFP and SRM does not yet support SMB3, creating new Time Machine backups is not possible in this environment.

so the answer is no, as I can confirm using a DS1819+. Existing backups continue, but I cannot create a new Time Machine disk on the DS1819+ using DSM 7.2.2

It is no longer possible to move a Time Machine backup. I don’t think it has ever been possible to merge backups.

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