Time machine : Using small SSD for frequent update + HDD for slower schedule
Yes, you can use multiple disks.  No, you can't specify a different set of backup targets by disk and they all get all data, so your smallest disk needs to accomodate all data.  

Though, you might be able to backup a full Time Machine config, alter it to trim out big volume directories, back up to SSD, restore full backup configs, backup to HDD, repeat.  Seems more work than worth it.  

And what happens if you run the small backup on your HDD by mistake?  Will Time Machine try to reclaim space on things that it doesn't see as needing backup?

A quick and dirty rsync script to copy critical stuff to SSDs might work better.