In Pathfinder there are numerous ways of obtaining 2x Claw Attack, such as Lesser Rage Totem, Feral Mutagen, alternate racial traits of Tieflings etc.
However, it seems that by specialising in getting claw attacks one could have 6+ Claw natural attacks while having only two hands and two legs. I guess the same would hold for bite or gore attacks.
RAW doesn't seem to mention that, but how about RAI?
Also, how does Rake monster special ability, that can be obtained with Beastform Alchemist interact with existing Claw attacks? Rake states that it grants additional Claw attacks, but can they be used at any time or only while grappling/pouncing, since there are separate Claw attacks listed?
Best Answer
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:
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.
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.