Separate Time Machine backups for different partitions
When you set a TM backup you specify which drive and partition to backup to. If you have an empty drive you can give it 3 partitions (or more) using disk utilities. Then when you back up your 3 partitions you can back each one up to a separate partition on the other drive. The real problem is that having three time-machine backups means your machine will almost always be backing up something. Since it backs up hourly I'd kick them off 15 minutes apart.
There are also extensions and apps that let you change the hourly backups to daily, or weekly. You could then back-up 10.5 on Wednesdays, 10.6 on Thursday, and 10.7 on fridays. Or back them all up once a day 7 days a week and separated the backups by 8 hours.