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The type of bonus is an Enhancement bonus, Enhancement bonuses do not stack unless they specifically say so as with the Crimson Sphere Ioun Stone (and it has a much higher price point you will notice).
It also says in its description that the stacking Enhancement bonuses max out at +6.
It has been answered in the FAQ that any +2 bonus to INT (confering a +1 difference in your final modifier) grants an associated skill with the item (making up for lost skill ranks) which you treat as always have max ranks into and an associated language.
If you already have ranks in this skill or already know the language, they overlap and you are not allowed to substitute for another one unless you specifically retrain them paying the retraining fees as normal per Ultimate Campaign.
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Okay to make the subject less confusing, I will try to break this down lol. A friend and I are having an argument on the rules of Ioun Stones, and their bonuses regarding stacking (he maybe right but I want to be SURE) because if I can get away with +18 INT... then by the gods I am damn well trying lol.
Okay... now I know bonuses from the "Same source" cannot stack, but considering the following stones have different bonuses would they truly count as the "same source"?
Crimson Sphere (+2 Intelligence bonus - can stack with other Crimson Spheres up to maximum of +6)
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Scarlet and Blue Sphere (+2 Intelligence bonus*) - max +6 with paying the gold and having the Craft Wonderous Item feat, + spell, etc via Advanced Ioun Stones**
* This stone has one skill associated with it, as a +2 headband of vast intelligence.
** http://www.d20pfsrd.com/magic-items/wondrous-items/wondrous-items/h-l/ioun- stones------
Magenta Prism (+2 to any one ability score) - max +6 via same method above
You left out a critical phrase in your summary. The various stones grant "enhancement" bonuses to each other (e.g., "This stone grants the wearer a +2 enhancement bonus to Intelligence"). Enhancement bonuses are the same type, and bonuses of the same type don't stack (with narrow exceptions).
The crimson sphere is one of those exceptions; it singles out that it stacks with other crimson spheres, up to a maximum of +6. But that doesn't mean it stacks with other enhancement bonuses, such as a scarlet and blue sphere.
So, basically, you can't do this (by rule).
There are always Inherent Bonuses to INT which can be gained by saving up and buy a Tome, but those usually aren't available until late game.
Lich Template adds +2.
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The headband also gives an enhancement bonus, so it won't stack with the stones. There is a book (Tome of Clear Thought) that gives an inherent bonus of up to +5, which would stack.
As your character ages, you get untyped bonuses to all your mental stats (at the expense of your physical ones) of up to +3.
So I think the following all stack
18 (starting store)
+2 (racial bonus)
+2 (lich template bonus)
+3 (age bonus)
+6 (enhancement bonus)
+5 (inherent bonus)
If you are willing to accept a mere 36 Intelligence.
Orfamy is right, the headband and Ioun stones don't stack. Getting +6 via magic items is already huge.
My question would be, where the heck do you get all the cash to buy this stuff? Sounds like a broken campaign to me. Not to mention a lich tending to be rather... er, evil and all, making him more likely as a monster/NPC than as a PC. Even if he were a Baelnorn (iirc those are neutral or good elven liches) I have a hard time seeing this as a PC.
But hey, it's your game. Having a 30+ INT score seems pretty godlike to me. The bonusses are staggering!
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I had a thread elsewhere about maxing ability scores, if you're curious. I got Intelligence up to 46, without age or the profane bonus from a Succubus, so 51 is a possibility, with the right choices.
And to save you the trouble, wishes and tomes that give "inherent" bonuses also don't-stack, the cap there is +5.
IIRC, there was even a specification in there that the 5 wishes had to be cast within minutes of each other to reach the +5 cap, or they wouldn't stack.
Anyway, anything about 18 or 20 INT is already superhuman. Beyond that it's just more math breaking the upper barriers of time and space. <g>
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if you have one or more level of Alchemist (Mindchemist) you can add in alchemical bonuses to INT with your Cognatogen... in fact,
Grand Cognatogen (Su): The alchemist's cognatogen now grants a +6 natural armor bonus, a +8 alchemical bonus to one mental ability score (Intelligence, Wisdom, or Charisma), a +6 alchemical bonus to a second mental ability score, and a +4 alchemical bonus to a third mental ability score. The alchemist takes a –2 penalty to his Strength, Dexterity, and Constitution as long as the cognatogen persists, and takes 2 points of ability damage to each physical ability score when the cognatogen ends. An alchemist must be at least 16th level and must have the greater cognatogen discovery or class ability before selecting this discovery.
Cognatogen gives a +4 bonus, Greater Cognatogen gives a +6 (at 10th level I think...)
It is only temporary... but the duration is 10 minutes per level...
You might also want to look at becoming a Lich thru Alchemy...
I think the lich template adds another +2, which isn't quite homebrew, but still pretty campaign-dependent
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18
+2 racial
+6 enhancement (Headband of Vast Intelligence)
+5 inherent (Tome of Clear Thought + 5 or Wish * 5 in close succession)
+5 untyped (Character Advancement - Level Ups)
+3 untyped (Age Effects - Venerable Age Category)
+2 untyped (Lich Template)
+8 alchemical (Alchemist 16 Discovery - Grand Cognatogen)
+2 untyped (Alchemist 20 Grand Discovery - Awakened Intellect)
+2 profane (Demon, Succubus - Profane Gift (Su))
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53 Intelligence total
There also seems to be a suggestion that you can get a +4 profane bonus from some creature, which would bring you to 55, but I cannot find it on the PRD, and can't access the SRD currently. There's also the mention of epic, which goes as high as it goes, mythic, which I'm not overly familiar with, and home-brew races, at which point you can do whatever you like anyways.
18
+2 racial
+6 enhancement (Headband of Vast Intelligence)
+5 inherent (Tome of Clear Thought + 5 or Wish * 5 in close succession)
+5 untyped (Character Advancement - Level Ups)
+3 untyped (Age Effects - Venerable Age Category)
+2 untyped (Lich Template)
+8 alchemical (Alchemist 16 Discovery - Grand Cognatogen)
+2 untyped (Alchemist 20 Grand Discovery - Awakened Intellect)
+2 profane (Demon, Succubus - Profane Gift (Su))
---------------------------
53 Intelligence totalThere also seems to be a suggestion that you can get a +4 profane bonus from some creature, which would bring you to 55, but I cannot find it on the PRD, and can't access the SRD currently. There's also the mention of epic, which goes as high as it goes, mythic, which I'm not overly familiar with, and home-brew races, at which point you can do whatever you like anyways.
So anyone but alchemists can go as high as 45 (assuming +4 profane and willingness to turn lich)...
Apparently non-alchemists and non-evil people get screwed :P (I wonder if the indication that evil people are smarter was intentional?)
43 for the non-alchemist. And, I don't think it was intentional so much as thinking people wouldn't min-max like this :P
...18
+2 racial
+6 enhancement (Headband of Vast Intelligence)
+5 inherent (Tome of Clear Thought + 5 or Wish * 5 in close succession)
+5 untyped (Character Advancement - Level Ups)
+3 untyped (Age Effects - Venerable Age Category)
+2 untyped (Lich Template)
+8 alchemical (Alchemist 16 Discovery - Grand Cognatogen)
+2 untyped (Alchemist 20 Grand Discovery - Awakened Intellect)
+2 profane (Demon, Succubus - Profane Gift (Su))
---------------------------
53 Intelligence totalThere also seems to be a suggestion that you can get a +4 profane bonus from some creature, which would bring you to 55, but I cannot find it on the PRD, and can't access the SRD currently. There's also the mention of epic, which goes as high as it goes, mythic, which I'm not overly familiar with, and home-brew races, at which point you can do whatever you like anyways.
So anyone but alchemists can go as high as 45 (assuming +4 profane and willingness to turn lich)...
Apparently non-alchemists and non-evil people get screwed :P (I wonder if the indication that evil people are smarter
The alchemist get two bonuses; a +8 alchemical and a +2 untyped from a discovery. That totals to +10. 53 - 10 = 43.
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...18
+2 racial
+6 enhancement (Headband of Vast Intelligence)
+5 inherent (Tome of Clear Thought + 5 or Wish * 5 in close succession)
+5 untyped (Character Advancement - Level Ups)
+3 untyped (Age Effects - Venerable Age Category)
+2 untyped (Lich Template)
+8 alchemical (Alchemist 16 Discovery - Grand Cognatogen)
+2 untyped (Alchemist 20 Grand Discovery - Awakened Intellect)
+2 profane (Demon, Succubus - Profane Gift (Su))
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53 Intelligence totalThere also seems to be a suggestion that you can get a +4 profane bonus from some creature, which would bring you to 55, but I cannot find it on the PRD, and can't access the SRD currently. There's also the mention of epic, which goes as high as it goes, mythic, which I'm not overly familiar with, and home-brew races, at which point you can do whatever you like anyways.
So anyone but alchemists can go as high as 45 (assuming +4 profane and willingness to turn lich)...
Apparently non-alchemists and non-evil people get screwed :P (I wonder if the indication that
Aye, but Lifat was taking account of the Lilitu, which offers a +4 profane bonus, as opposed to the Succubus' +2, increasing it back up to 45. I only included the +2 originally as I didn't have access to the SRD at work, and hence couldn't verify the Lilitu.
Liches don't qualify for Profane Gift. You have to be humanoid.