Weapons like the Amputator, Cold Iron Vanquisher, etc. are supposed to trade slightly lower base damage for a damage boost against one specific family while still dealing Normal damage and thus being effective against all enemies. It is supposed to be a sort of compromise between a Special damage weapon and a full Normal weapon like the Leviathan Blade.

However, the problem with weapons like these is that damage boosts are capped at +6, and the damage boost against a specific family is counted in the same stack as general damage boost. This means, for example, if you already have +6 sword damage from your armor and other equipment, then the innate damage boost on the CIV no longer does anything, and a Leviathan Blade would be 100% superior.

This is an issue that results from the way stat boosts are handled by the game. The most elegant solution would of course be to make the family damage bonus stack separately from the general/weapon-class damage bonus. However, this might require tinkering around in lower level game code and we all know OOO isn't up for that these days.

But there is another solution which works within the current game systems and only requires changing the data tables for the weapons' stats. Instead of having a damage boost against the desired family, give the weapon abnormally high base damage, but also a damage penalty against all other monster families.

For example, suppose the Acheron deals 200 damage (100 Normal, 100 Shadow), then its damage values are as follows:

Vs. Slimes and Gremlins: 240 damage

With + 6 damage boost: 298 damage

Vs. Contructs and Beasts: 200 damage

With +6 damage boost: 248 damage

Vs. Fiends and Undead: 120 damage

With +6 damage boost: 149 damage

In order for the Amputator to be useful, it should be at least on par with the Acheron against Slimes so we give it 240 base damage but MAXIMUM (-6) damage penalty against all other families. This results in the following damage values:

Vs. Slimes: 240 damage

With +6 damage boost: 298 damage

Vs. Everything else (innate -6): 182 damage

With +6 damage boost (total +0): 240 damage

This makes it so the Amputator is fully on par with the Acheron against slimes, but deals slightly less than the vs. neutral damage of the Acheron as its "normal" damage, and so lives up to its intended purpose.

For another example, let's look at the Leviathan Blade vs. CIV. Suppose the Leviathan Blade deals 200 damage:

Vs. Everything: 200 damage

With +6 damage boost: 248 damage

We want the CIV as good as an Elemental weapon against the Undead, which is the same as the damage of the Acheron vs. enemies weak to Shadow, while being weaker than the Leviathan Blade against everything else:

Vs. Undead: 240 damage

With +6 damage boost: 298 damage

Vs. Everything else (innate -6): 182 damage

With +6 damage boost (total +0): 240 damage

This does leave a slight loophole, in that by giving the weapon abnormally high base damage but innate -6 damage penalty, it effectively raises the damage boost cap of the weapon to +12 rather than +6. So if you were somehow able to get +12 sword damage, the new CIV would deal 298 damage (same as super-effective) against everything. This might be too much so alternatively the numbers could be adjusted to lower the base damage by having +3/-3 damage bonus/penalty. In that case, the CIV's damage numbers would look like this:

Base damage: 214 damage

Vs. Undead (innate +3): 240 damage

With +6 damage boost (total +6): 265 damage

Vs. Everything else (innate -3): 188 damage

With +6 damage boost (total +3): 240 damage

With +9 damage boost (total +6): 265 damage

With +12 damage boost (total +6): 265 damage

This would leave the family bonus Normal weapons ultimately weaker against the enemy it is specialized against than Special damage weapon. However, it is perhaps more balanced as it only has an effective bonus cap of +9 rather than +12 and so although a fully boosted CIV is now superior to the Leviathan Blade, it still deals less damage than a Special damage weapon against its super-effective monster types.