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I was looking through the core spells and found the Paladin Spell Holy Sword, which states specifically that it overpowers whatever magic spells or enhancements that are placed on it. While this is fine and good, no other spell has this stipulation. As such, I have two questions:

  1. If three creatures in the same party each cast Greater Magic Weapon on the same quiver of arrows, does that mean that the arrows get the net bonuses granted by the three spells or does each cast after the first reset the duration of the spell?

  2. If the same three creatures each cast a different buffing spell on the same bow, does that grant a net bonus, or would the last spell be the only one that counted?

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  1. Greater magic weapon applies an enhancement bonus, that is, a bonus with the enhancement type. Bonus types are very important, because they are the way the game answers these kinds of questions (whether the bonuses come from spells, items, feats, or whatever).

    In this case, the arrows are affected by three spells, and thus three enhancement bonuses, but those bonuses overlap, rather than stack. The arrows simply use the highest one. The fact that all three spells still apply can be important, however, if one of them were to end prior to the others, for example if they were cast at different times or one is dispelled.

    Even if greater magic weapon did apply an untyped bonus, rather than an enhancement bonus, it would still overlap and not stack, because of the same-source rule (“Bonuses without a type always stack, unless they are from the same source,” from the above link).

  2. As long as the bonuses are of different types (or untyped from different spells), then yes, they stack.

    They can also apply simultaneously, even if they have the same type or come from the same spell, if they do different things: if one spell gives an enhancement bonus to attacks with a weapon, while a separate one gives an enhancement bonus to damage rolls with the weapon, they don’t interfere with one another. This isn’t really “stacking” since the two things are just completely separate. Either or both of these hypothetical spells would overlap (not stack) with greater magic weapon, which does both.

  3. You didn’t ask, but about holy weapon: it is, as you note, rather special in that while it applies to a weapon, it wipes out all other magic on the weapon. This basically means that you treat the target weapon as being a masterwork weapon of its type made of its material, ignoring all built-in magical enhancements as well as any other spells cast upon it. In some situations, this could even be used offensively, to weaken an enemy’s weapon (if you are Good, the effects of holy sword are less dangerous to you than the effects of any weapon that has a +5 enhancement as well as literally anything else).

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You're missing the more general rule here, which is that in Pathfinder the same type of bonus does not stack. See the Bonus section of the SRD for an explanation of how bonuses work.

The important aspect of bonus types is that two bonuses of the same type don't generally stack. With the exception of dodge bonuses, most circumstance bonuses, and racial bonuses, only the better bonus of a given type works. Bonuses without a type always stack, unless they are from the same source.

In this case, GMW provides an "enhancement bonus," so it does not stack with other enhancement bonuses - from other GMWs, enhancement bonuses from the weapon being enchanted in the first place, etc. It would stack with another weapon buff that provided a different type of bonus (sacred, competence, etc.).

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