They strike 4 times, extra hands doesn't add extra attacks.
Vestigial Arm specifically states it does not give you any extra attacks, but can be used to wield a weapon. That means get the same number of attacks as someone with only two arms. You can use the dagger in the third arm as part of the attack, but it does not do anything that a person with two arms cannot do.
Benefit: The alchemist (read: Mutation Warrior) gains a new arm (left or right) on his torso. The arm is fully under his control and cannot be concealed except with magic or bulky clothing. The arm does not give the alchemist any extra attacks or actions per round, though the arm can wield a weapon and make attacks as part of the alchemist’s attack routine (using two-weapon fighting). The arm can manipulate or hold items as well as the alchemist’s original arms (for example, allowing the alchemist to use one hand to wield a weapon, another hand to hold a potion, and the third hand to throw a bomb). The arm has its own “hand” and “ring” magic item slots (though the alchemist can still only wear two rings and two hand magic items at a time).
Special: An alchemist may take this discovery up to two times.
The arm just allows the mutation warrior to attack but it doesn't give him an extra attack. You attack with the vestigial arm, you lose an attack from the secondary arm.
So the total amount of attacks you can take at lvl 6 is 4.
Ah, I get the point. Thank you guys.
That is to say, a 4-handed mutagen warrior can wield two two-handed weapons, each weapon by a regular hand and a vestigial hand?
I think so. Not really worth spending 2 discoveries on vestigial arms for TWF with two handed weapons imo. You still need to spend all those feats, have high dex and in general the dmg increase isn't that great. Makes for cool visual though.
Vestigial arms gives you more options as to what you can hold, but not any more attack economy. Lets say, to illustrate, you have an Alchemist with +11 BAB (3 iteratives), and two vestigial arms. Even if you're wielding four different weapons, one in each hand, you still attack 3 times normally, but you can assign any of the four weapons to those three iterative attacks. Even if you are wielding two two-handed weapons using your four hands, you still only attack 3 times, but you have your choice of two weapons to swing each time, each of which has different properties to work better against certain foes. If you decide to use TWF rules to gain additional off-hand attacks, you might have several different weapons from which to choose. Say you have a pair of morningstars, a cestus, and a dagger. They are made of a variety of materials and have a variety of enchantments on them. You would still pick just two of them to use for a TWF routine. But, at the same time, you'd threaten with all of them as well. Or you might use a longspear, morningstar, and cestus. You'd threaten at reach with the longspear and threaten adjacent with the other two. You'd still have a variety of weapons to use. Or you might use a shield along with TWF. The arms only grant additional options of what you can hold or additional weapons from which to choose when you make your attacks. But, just as a two-armed character can't fight with a 2-h weapon plus an off-hand, an alchemist with two additional arms can't either.
Incorrect on the bolded part.
When it comes to TWF, you can only ever assign two weapons to fulfill the two sets of iteratives that TWF grants you. You can't ever substitute weapons in-between attacks, even if they are, in fact, exactly the same (such as by using more than 2 +1 Javelins to throw at enemies via TWF), nor can you use those hands required (or being metaphorically used) to fulfill the other attacks being taken via TWF, such as by switching from a throwing weapon to another throwing weapon, or by switching grip on a two-handed weapon to draw a one-handed weapon and attack.
Do I think it's a silly rule? Yes, it is a little. But per the TWF FAQ (and by extension the Armor Spikes FAQ), that's how it works.
The FAQ actually clarifies the opposite.
For regular iterative attacks, yes, you can substitute weapons in-between attacks.
You can't for TWF.
Look at the examples it gives. Here's the standard attack example:
...Let's assume you're a 6th-level fighter (BAB +6/+1) holding a longsword in one hand and a light mace in the other. Your possible full attack combinations without using two-weapon fighting are:
(A) longsword at +6, longsword +1
(B) mace +6, mace +1
(C) longsword +6, mace +1
(D) mace +6, longsword +1......If you have Quick Draw, you could even start the round wielding only one weapon, make your main attack with it, draw the second weapon as a free action after your first attack, and use that second weapon to make your iterative attack (an "iterative attack" is an informal term meaning "extra attacks you get from having a high BAB").
So, from this, we get 4 possiblities, and the option to draw a weapon in-between our full attack action to complete the iterative.
Now, we have the TWF attack example:
...Using the longsword/mace example, if you use two-weapon fighting you actually have fewer options than if you aren't. Your options are (ignoring the primary/off hand penalties):
(A') primary longsword at +6, primary longsword at +1, off hand mace at +6
(B') primary mace at +6, primary mace at +1, off hand longsword at +6In other words, once you decide you're using two-weapon fighting to get that extra attack on your turn (which you have to decide before you take any attacks on your turn), that decision locks you in to the format of "my primary weapon gets my main attack and my iterative attack, and my off hand weapon only gets the extra attack, and I apply two-weapon fighting penalties."
It effectively tells us "You can do the following with the TWF action." Notice how it only gives us two methods of carrying out the TWF action, none of which tell us the same option to draw a weapon mid-attack, nor of the ability to switch between weapons for your attack regime.
In addition, from the above options, there is no "primary longsword +6/primary mace +1/off hand longsword +6" combination, nor is there an inverse of that, and this is evidenced by the FAQ stating "if you use two-weapon fighting, you actually have fewer options than if you aren't [two-weapon fighting]." If we went with your interpretation that it "clarifies the opposite," then I should be able to do either of those options. But they're not a valid option that was listed in the FAQ, meaning the odds of them actually being valid is pretty slim.
There's also the Armor Spikes FAQ. No, I'm not bringing it up because of the unwritten rule. I bring it up because of this:
Likewise, you couldn't use an armored gauntlet to do so, as you are using both of your hands to wield your two-handed weapon, therefore your off-hand is unavailable to make any attacks.
If the sole intent of Armor Spikes not working with a Two-handed Weapon in regards to TWF is because of the unwritten rule, the above statement wouldn't be present, and I could, for example, TWF with a Spiked Gauntlet and a Longbow (via Point Blank Master and Snap Shot feat chain).
I highly doubt the above sentence was placed to mean absolutely nothing; Paizo isn't (always) that stupid or careless in its sentence structure and application. It makes more sense to say that it provides the concept that your hands are occupied for the entirety of the TWF action. It would explain why the above example with the bow and spiked gauntlet would not work, even though it does not break the unwritten rule.
