Use folder (rather than partition) for Time Machine backups?

I'm trying to get a more flexible structure on the external drive I use for Time Machine and Carbon Copy Cloner backups.

Currently, I have it set with three partitions - one for TM, another for CCC, and the third as a 'dump' space' for temporary items and into which I sometimes drag stuff I want to keep a temporary backup of whilst deciding its longer-term fate.

Having read that CCC can be set to use a non-root folder on a drive or partition, I wanted to do the same with TM. That way, I'd not need to partition it and hence have maximum flexibility on how I used the space - more so than if I set hard limits on the partitions.

But, TM seems to only offer the option of using a drive or partition rather than a folder, and so in using an unpartitioned drive it'll create and use a folder named 'Backups.backupdb' in the root - which is less elegant/helpful than something I could choose... like 'TM backups from iMac'.

Whilst this isn't a major issue, is there a way to do this?