There's nothing about this in RAW, as you suspect.
This was discussed on the paizo boards as well. The closest rule you get is from the Eidolon Claw Evolution:
Claws (Ex): An eidolon has a pair of vicious claws at the end of its limbs, giving it two claw attacks. [...] This evolution can be selected more than once, but the eidolon must possess an equal number of the limbs evolution.
If weird outsiders that can resemble anything the Summoner's player can think of can't have multiple claws per arm, a point can be made that "normal" creatures also can't.
Rake is a different thing. Rake allows you to make 2 free claw attacks during a grapple, in addition to whatever you do in the grapple, including regular claw attacks.
Rake (Ex): A creature with this special attack gains extra natural attacks under certain conditions, typically when it grapples its foe. In addition to the options available to all grapplers, a monster with the rake ability gains two free claw attacks that it can use only against a grappled foe.
The Beastmorph Alchemist gains Rake without a Claw specified, so you can use any claws you possess (if you have multiple limbs) for the ability.
There are no rules regarding over-sized weapons and using more than two arms. Normal over-sized weapon penalties apply.
Inappropriately Sized Weapons: A creature can't make optimum use of a weapon that isn't properly sized for it. A cumulative –2 penalty applies on attack rolls for each size category of difference between the size of its intended wielder and the size of its actual wielder. If the creature isn't proficient with the weapon, a –4 nonproficiency penalty also applies.
The measure of how much effort it takes to use a weapon (whether the weapon is designated as a light, one-handed, or two-handed weapon for a particular wielder) is altered by one step for each size category of difference between the wielder's size and the size of the creature for which the weapon was designed. For example, a Small creature would wield a Medium one-handed weapon as a two-handed weapon. If a weapon's designation would be changed to something other than light, one-handed, or two-handed by this alteration, the creature can't wield the weapon at all.
The rest of this answer assumed multiple greatsword (or other two handed weapons).
You cannot use the Two-Weapon fighting feats if you are using more than two arms. You need to use the Multi-weapon fighting feats. If you were fighting with two greatswords, one of them with be primary, the other offhand. Likewise, if you had sixarms, two for the weapons would be offhand, and so on. You will always have one primary weapon.
Multiweapon Fighting (Combat)
Prerequisites: Dex 13, three or more hands.
Benefit: Penalties for fighting with multiple weapons are reduced by –2 with the primary hand and by –6 with off hands.
Stealing the table from this answer you would make your all your attacks at -4 regardless of if they were off-hand or primary:
Table: Multi-Weapon Fighting Penalties
Circumstances Primary Hand Off Hand
Normal penalties –6 –10
Off-hand weapon is light –4 –8
Multi-Weapon Fighting feat –4 –4
Off-hand weapon is light and
Multi-Weapon Fighting feat -2 –2
I have found no rule which changes the damage modifier (*1.5) from high strength.
Likewise, power attack applies to all attacks as described, there are no special rules for using more than one two handed weapon. The primary great sword would get +3 per -1 penalty. The off hand greatsword would get +1.5 per -1 (rounded down, so +1, +3, +4, +6, etc. )
Emphasis all mine.
BONUS HOUSERULE:
I would not allow a creature to use a weapon who's category was more than two handed, as per the normal rules. However there are items in 3.5 that required more than two hands to use ( I think it was the scissor sword ) and had better stats.
I would also allow a creature with more than two hands to substitue the Multi-WF feat in place of the T-WF for classes with bonus feats, such as ranger.
Have a look at the Gythka and Scissors Sword, which are four handed and six-handed weapons from Savage Species (I know, not pathfinder) on page 45.
Best Answer
The Official Pathfinder FAQ explicitly has covered this discovery (and the use you are suggesting) and has stated that:
Bolding mine. Effectively, if you add natural weapons to the vestigial arm, you can use them only in place of other attacks, and you can never gain any additional attacks under any circumstances.