Do you need to partition the drive?
I do pretty much what you're suggesting. My plug-in drive has one partition, and four folders on it, called "Laptop", "Desktop", "Old Machine" and "Linux box".
The backup routines on each machine know which folder to use. Within that folder, they create a new folder with the backup date, then copy everything I want backed up into that folder.
When the drive starts to get full, I delete the "in between" backups and keep a selection. Some, I archive off to DVDROM.
Defragging it occasionally is a good idea, too.
I've only used the backup to restore a couple of times in ten years, but it was a lifesaver at the time.