Multiple archetypes can never be applied to the same character if they replace the same base ability. So no, those two would not stack.
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Multiple archetypes can never be applied to the same character if they replace the same base ability. So no, those two would not stack.
In this case though, each one replaces the base "Smite Evil" with...
Smite Evil.
Here is the base ability:
Smite Evil (Su): Once per day, a paladin can call out to the powers of good to aid her in her struggle against evil. As a swift action, the paladin chooses one target within sight to smite. If this target is evil, the paladin adds her Charisma bonus (if any) to her attack rolls and adds her paladin level to all damage rolls made against the target of her smite. If the target of smite evil is an outsider with the evil subtype, an evil-aligned dragon, or an undead creature, the bonus to damage on the first successful attack increases to 2 points of damage per level the paladin possesses. Regardless of the target, smite evil attacks automatically bypass any DR the creature might possess.
In addition, while smite evil is in effect, the paladin gains a deflection bonus equal to her Charisma modifier (if any) to her AC against attacks made by the target of the smite. If the paladin targets a creature that is not evil, the smite is wasted with no effect.
The smite evil effect remains until the target of the smite is dead or the next time the paladin rests and regains her uses of this ability. At 4th level, and at every three levels thereafter, the paladin may smite evil one additional time per day, as indicated on Table: Paladin, to a maximum of seven times per day at 19th level.
And here is the Hospitaler:
Smite Evil (Su): This functions as the paladin ability, but the hospitaler can smite evil one additional time per day at 7th level, and every six levels thereafter (instead of 4th level and every three levels thereafter).
And here is the Sacred Servant:
Smite Evil (Su): This functions as the paladin ability, but the sacred servant can smite evil one additional time per day at 7th level, and every six levels thereafter (instead of 4th level and every three levels thereafter). This replaces smite evil.
I would say that they can stack.
Also note, the Hospiraler version does not have the text "This replaces smite evil."
Multiple archetypes can never be applied to the same character if they replace the same base ability. So no, those two would not stack.In this case though, each one replaces the base "Smite Evil" with...
Smite Evil.
Here is the base ability:
Smite Evil (Su): Once per day, a paladin can call out to the powers of good to aid her in her struggle against evil. As a swift action, the paladin chooses one target within sight to smite. If this target is evil, the paladin adds her Charisma bonus (if any) to her attack rolls and adds her paladin level to all damage rolls made against the target of her smite. If the target of smite evil is an outsider with the evil subtype, an evil-aligned dragon, or an undead creature, the bonus to damage on the first successful attack increases to 2 points of damage per level the paladin possesses. Regardless of the target, smite evil attacks automatically bypass any DR the creature might possess.
In addition, while smite evil is in effect, the paladin gains a deflection bonus equal to her Charisma modifier (if any) to her AC against attacks made by the target of the smite. If the paladin targets a creature that is not evil, the smite is wasted with no effect.
The smite evil effect remains until the target of the smite is dead or the next time the paladin rests and regains her uses of this ability. At 4th level, and at every three levels thereafter, the paladin may smite evil one additional time per day, as indicated on Table: Paladin, to a maximum of seven times per day at 19th level.
And here is the Hospitaler:
Smite Evil (Su): This functions as the paladin ability, but the hospitaler can smite evil one additional time per day at 7th level, and every six levels thereafter (instead of 4th level and every three levels thereafter).And here is the Sacred Servant:
Smite Evil (Su): This functions as the paladin ability, but the sacred servant can smite evil one additional time per day at...
Whichever you tried to apply first would be considered an ability of the archetype and not the base class, regardless of them having the same name. An archetype replaces the base class ability, so Hospitaler smite evil cannot be replaced with Sacred Servant smite evil or vice versa. The two archetypes cannot be combined.
They do not stack as both change or replace the same ability.
Hospitaler and Sacred Servant both replace Smite Evil with a weaker version (@ 7th, and every 6 levels after). The text is identical. Could these archetypes stack?
It would not make sense for them to stack. The idea seems to be that the archetypes compensate for the weaker smite with other abilities. If you take both, then you are getting double compensation, which would probably be unfair. That is, you would presumably be stronger than, not balanced with, the standard paladin - even with the weaker smite.
So nope.
RAW, if they modify the same ability, they do not stack.
This is 100% not legal for PFS. There is no doubt about this.
That said, if it's for a home game, ask your GM.
