Yes I know that crossblooded and wildblooded don't stack, courtesy of this FAQ, but for argument's sake (and the fact that a LOT of home games do let them stack) let's let them stack. How would an Empyreal/Sage crossblooded sorcerer cast spells? Would they be based off of both their Wisdom and Intelligence? What happens when those values are different?
Curious as to what other people think
Relevant bits:
Crossblooded Archetype
Empyreal Bloodline
Sage Bloodline
You would replace charisma with wisdom/intelligence, and then replace that with intelligence/wisdom.
Both say "You use your ___, rather than Charisma" though so BadBird, your logic doesn't quite hold up. It'd be easy enough to say that whatever is higher is the one that you use if it said may (like with using both Guided Hand and Weapon Finesse) but both bloodlines explicitly replace Charisma, so one couldn't replace the Wisdom or Intelligence casting of the other. In the case of if it was an optional ability score change then one could stay as Charisma and the other override it without a problem, but such is not the case.
Since both powers work by "instead of", I'm going by the substitution principle. If you replace X with Y, then anything that would affect X affects Y. So, replace X with Y, and then replace Y with Z. There's no grounds for taking two 'use this instead of that' clauses and getting to use both as far as I can see. Others may disagree.
I personally don't see it as replace X with Y and then replace Y with Z. It looks to me like it should be replace X with either Y or Z (player's choice), but as to whether they replace actually it with Y or Z is left in some quantum state until it actually becomes relevant. A question that's left with my interpretation is whether or not they get to choose on the fly. For example, if one of these characters gets hit by a feeblemind spell, are they able to use Wisdom to cast spells if they've been using Intelligence up until then?
So the actual rules say it doesn't work because it creates problems. And then you ask "by the rules" how does this work if we ignored that first rule?
The answer is it doesn't. If you want an answer you will have to ask your GM.
I'm not even sure why you would want to take both, as the ability score replacement is usually what people are after, and why would you replace it twice.
At best you would get to choose either your wisdom or int to base your spellcasting off of. But what would be the benefit of being able to choose one or the other when you can just take the one bloodline you want in the first place?
This is supported by the rules.
It works just like Ki Pool. If you have a Ninja/Monk, you don't get CHA+WIS to your Ki Pool. You need to choose attribute to govern it.
I imagine the same applies here.
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For example, if one of these characters gets hit by a feeblemind spell, are they able to use Wisdom to cast spells if they've been using Intelligence up until then?
No. "The affected creature is unable to use Intelligence- or Charisma-based skills, cast spells, understand language, or communicate coherently." Doesn't matter if you're a Wis-based caster, you can't cast.
As for whether you could swap casting stats when under the effect of, say, ability damage, GM's call but probably not. I would probably allow the bloodline combination but require you to pick your casting stat at level 1 and stick with it. That's also how the ki pool works:
If the ninja possesses levels in another class that grants points to a ki pool, ninja levels stack with the levels of that class to determine the total number of ki points in the combined pool, but only one ability score modifier is added to the total. The choice of which score to use is made when the second class ability is gained, and once made, the choice is set.