Can I move Time Machine files from an external disk, reformat it, then restore the TM files?
You can make an efficient copy of the Time Machine volume by using Disk Utility and making a disk image of the original volume. Store that image on the temporary storage / other drive as a single file. Once you've erased the original drive and partitioned it as you wish, then use Disk Utility to reverse the operation and restore the image to the new partition. That will erase anything on the new partition so do the restore first then add extra files as needed.

Time Machine will pick up and use the new destination and carry on with backups and cleanup operations assuming no corruption happens during the two copy events.



I would just get a cheap drive and do the first step. Once I've verified that the backup img file mounts and I can restore a sample file to my desktop from Time Machine, I'd just erase the intended drive and start over with backups.

Much easier that way and why spend the second half of the work - just archive that Time Machine data offline in case you need it down the road.