Start new backup folder for same device while preserving previous backups?

Time Machine (TM) is designed to append backups of devices with the same name and identifiers to an existing backup set. It may be simpler to get another backup drive and start a new TM backup set, while keeping the old drive as an archive.

However, it may still be possible to do what you are asking, but understand, if your backups are critical to you, you will be doing so at your own risk. Note: Be sure that your current backup disk has enough space for what will be two TM backup sets.

There are two basic steps:

1. Rename the current backup set.
2. Start a new backup.

For the first step:

1. Connect the external drive to your Mac.
2. Navigate to the Backups.backupdb folder at the root of your TM drive.
3. Inside this folder, locate the subfolder with your Mac's name. For example, MyMacBook.
4. Rename the old backup folder to something like MyMacBook-Old. This will prevent TM from recognizing it as an active backup.

For the second step:

1. Open System Settings > General > Time Machine.
2. Remove the current TM disk from the list by clicking the - button.
3. Add the same disk back by selecting it as the TM destination. With the old folder renamed, TM will create a new folder for the new backup.
4. Start the backup process as usual. A new folder matching your Mac's name will be created.

The most conservative and foolproof way to accomplish what you seek is to obtain an additional backup drive. Disconnect the existing one and set it aside until such time you decide it's no longer needed.

Reasons are many, not the least of which is that TM is not designed to do what you're proposing.

Here I say you have two choices:

1. Get another drive as I mentioned, or
2. Contact Apple Support directly for further assistance with this matter or wait for someone else who may have a potential solution for you.