I propose a Rainbow Brandish line upgrade path to follow the Cautery Sword 3* upgrade all the way to 5*. The sword should continue the normal damage line that the Cautery has, as well as adding more family damage bonuses and retaining it's normal damage.
3* - Cautery Sword - Red/White stripes, Damage bonus vs slimes
4* - - Red/White/Yellow stripes, Damage bonus vs slimes, beasts, fiends. (Subject to change)
5* - - Red/White/Yellow/Blue stripes, damage bonus vs all families. (Yes)