In Pathfinder 1E, how do Greater Magic Fang and Amulet of Mighty Fists stack

Question

My animal companion has an Amulet of Mighty Fists that only gives me, say, +1, Frost, without any enhancement bonus. So it's a +2 equivalency, with a +1 enhancement bonus.

Let's say that I then cast a Greater Magic Fang which would grant a +3.

I can see any of the following things happen.

1. Nothing -- there's already an enhancement situation.
2. No more Frost. It's now a +3 enhancement bonus with no special abilities.
3. +3/Frost -- it takes the greater of the two enhancement bonuses and keeps the special abilities.

Honestly I can accept see any of these. Right now we're playing that it's the recipient's choice of 1 or 2. Any opinions?

Answer 1

It's #3

Assuming nothing else about the animal companion, if the animal companion wears a frost amulet of mighty fists, then the companion is the subject of a greater magic fang spell so that its natural weapon gains a +3 enhancement bonus, the animal companion benefits fully from both the amulet and spell.

(Unlike a typical magic weapon—see here—the amulet specifically says that it does not first need to grant a +1 enhancement bonus before it can grant magic weapon special abilities, so a frost amulet of mighty fists that grants no enhancement bonus is a legit standalone item.)

The magic weapon special ability frost from the amulet is priced as a +1 enhancement bonus and that +1 enhancement bonus counts toward the +10 maximum virtual enhancement bonus that a weapon can possess ("A single weapon cannot have a[n]… enhancement bonus plus [magic weapon] special ability bonus equivalents… higher than +10"; see here). However, the magic weapon in question—the animal companion's natural weapon—doesn't have an actual numeric enhancement bonus until the greater magic fang spell, so the greater magic fang spell functions normally and completely, granting its full bonus to the natural weapon.

Were this instead a +1 frost amulet of mighty fists, the greater magic fang spell's numeric enhancement bonus would overlap with the amulet's numeric enhancement bonus, and only the bigger enhancement bonus would apply, hence still just the +3. Further, the amulet's frost weapon special ability would continue to function normally in this case, too.

Answer 2

Equipment can benefit from multiple enhancements

With certain exceptions, a weapon can benefit from multiple enhancements. The same principle applies to unarmed strikes and natural attacks. Abilities and benefits add together, but there are certain exceptions and limitations.

• Enhancement bonuses do not stack. Bonuses of the same type do not stack, enhancement bonuses are no exception. The highest bonus would apply, as indicated by the core rulebook.

• Special abilities of differing types stack. So, frost and flaming stack, but not multiple instances of either of these abilities. This rule also applies to abilities that function as other abilities. So, adding flaming to a flaming burst will provide no additional benefit.

  There's no rules that say adding new special abilities causes existing ones to disappear, and there's plenty of NPC statblocks (like this) that cast greater magic weapon on a weapon that already has special abilities

• The bonus equivalency can never exceed +10. This is a hard cap for all weapons. See this FAQ.

Bonus equivalency only applies for determining the price of a magic weapon. Aside from the +10 hard cap, it's irrelevant for determining how multiple enhancement effects stack on a magic weapon.

This NPC has a canonical example of a +1 unholy cold iron falchion that turns into a +3 unholy cold iron falchion with an oil of greater magic weapon.