Time machine is ready to back up every Mac-formatted drive attached to your Mac onto a backup drive. By design, it has ONE exclusion list which is used for every backup operation.
It can have additional backup drives added, and each will be used (in rotation) to create separate, stand-alone Backup set(s) independent of the other sets on other drives. (But still using the ONE exclusion list.)
Once the initial backup of everything has been done, Time Machine runs about hourly and does an incremental backup of only the files changed since the last backup.
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To accomplish something similar to what you want, you could use a 'concatenated RAID' also known as Just a Bunch of Drives [pasted together into a MegaDrive] or JBOD to have a destination set large enough to hold your complete backup set and still be affordable.
The increment backup feature would keep each Time machine run reasonable.