Diablo – Helltooth 6-piece set bonus, does it apply to existing pets or only on recast

Unless the bonus is identified on the items, no. In your example, putting on four pieces of Cain's Fate would not give you an additional bonus over putting on three pieces.

If, for example, you picked up a set that had bonuses for 4 or 5 pieces, then these sets would give additional bonuses as detailed on the items for equipping more pieces of the set.

So I found out for the first part.

I found an easy testing method. Although my raw DPS was too random to test anything, I could use a little trick.

If you don't know, hydra have a fixed attack speed and damage. Each of the head make the same damage and it takes everything into account (even your attack speed while hydra's AS remains the same) The damage of the heads is calculated when cast. That means hydra damage is fixed and very reliable.

The test method is as follow. I only equipped the weapon (which does +25% bonus damage against beasts). So I found myself with a really low DPS and fixed damage (when it doesn't crit, but even crit damage are fixed). Then you need to run and/or have a friend to tank things.

I tested the damage on different type of mobs. Those with which I don't have any bonus and beasts mobs. I did 36 599 damage when no bonus and 45 749 to beasts, which is exactly +25% damage. I then tried hitting different type of elite beast-like mobs (elite with the same model than beasts, but without the beast affix). On unique, yellow and blue I did 45 749 damage, which means the +25% bonus applied on them. That also means elite keeps the type their model belongs to, they just doesn't show it in the affix. So, yeah, bonus damage against {Mob type} apply to elite mobs of the same type.

As a side note, this also means "Pig Sticker" (+X% dmg against beats/human) and Tyrael (+X% damage against demons) can be more powerful than anything else because they provide a big bonus you don't find anywhere else, and which works against elite. I need to find item who does bonus damage against undead and reaper now.

Edit:

Now, the secondary question: How does "Bonus damage against Beasts" interact with "Bonus Damage against elite"? Additively or multiplicatively?

Just to explain, I'm wondering about that second question because we can think: - dmg vs Beats and dmg vs elites are two distinct bonus and thus should be multiplicative. OR - dmg vs Beats and dmg vs elites are both dmg vs {mob type}, they are the same bonus and so are additively.

So, I tested with the same method using "Pig Sticker" (+25% against beasts) and "Unity ring" (+4% against elites). The results are as follow: - Undead: 72 207 dmg - Beast: 90 259 dmg - Elite Beast: 93 870 dmg

Basically, that means I did +25% damage against beast compared to undead. +4% damage to elite beast compared to beast. and +30% damage to elite beast compared to undead.

So yes: "Bonus damage against {mob type}" and "Bonus Damage against elite" are considered two different type of bonus for the game. And so they stack multiplicatively. (1.25 * 1.04 = 1.30)