An animal companion with only one natural weapon gets a second attack with it at a -5 penalty (basically just like an iterative attack) when the companion would normally gain the Multiattack feat.
Is this a Pathfinder rule? Its not a 3.5 rule. Multiattack does ONE thing, and ONE thing only. It reduces the penalty on secondary natural attacks by 3 (down to -2, from -5). Nowhere in its description does it give any extra attacks. Rapid Strike DOES give you an extra attack, put it only works with a "pair" of weapons like a set of claws or wing buffets or tentacles, and it only gives one extra attack per "pair" so it wouldn't work with a bite. Bites DO often have special rules if they are the sole natural weapon, in that they sometimes deal 1.5x +str damage similar to attacking with a two handed weapon. They do NOT benefit from 2:1 Power Attack like wielding a two handed weapon though.
Also, there are some spells, psionic powers, and class features that give you natural weapons, but have you use your BAB and iterative attacks with them, instead of the normal rules. I can't think of any at the moment, but I could try to find examples if you really, really want me to.
I actually can't think of any. The abilities that give you weapons (Flame Blade, Ice Axe, Thunderlance, etc) all give you iteratives. The ones that give you natural weapons (Claws of the Beast, Bite of the Wolf, Trollshape, Body of War, etc) all explicitly give you natural attacks that follow all of the rules for natural attacks.
You are right in the advantage though. Its much easier to load up on natural attacks then to get manufactured weapon attacks. A Silverbrow Human Totemist3 with Aberrant Blood + Inhuman Reach + Deepspawn who binds Girallon Claws to his Totem and shapes Dragon Tail can make 7 natural attacks in a round (4 claws, 2 tentacles, 1 tail). A Warforged Totemist3 with Second Slam and Jaws of Death feat could have 7 (2 slams, 1 bite, 4 claws). If either of those took a flaw + Improved Unarmed Strike, then they could make 8 attacks (1 UAS primary, 7 natural attacks secondary).
The easiest way to arbitrate natural weapons is first to determine if the wielder is wielding a weapon that can make iteratives. This is a manufactured weapon or UAS. If not, then figure out what it's primary natural weapon is. Monster stat blocks usually indicate this, but PC abilities generally don't indicate it. If it isn't clear, just pick one. This attack gets full +Str bonus on damage. All other attacks are secondary and suffer a -5 to hit (-2 with Multiattack). If there is a weapon that can make iteratives, ALL natural weapons become secondary(-5 to hit and +1/2 Str bonus). Then you make your normal iterative sequence (which may or may not include TWF) and THEN you add on all of your natural weapons, AS LONG AS YOUR WEAPONS AREN'T INTERFERING WITH YOUR NATURAL WEAPONS. For example, if you are holding a sword in your clawed hand, you can't make a claw attack with that hand.
Simple simple!
