Can I make more Pistol shots per round if I have additional arms in Pathfinder?

Question

I was thinking about building and Unchained Eidolon (Azata) for using Firearms. The thing is, increasing the number of arms (limbs) is trivial for Eidolons, as is taking a Pistol in each hand, or a Musket in each pair of hands. Will it increase the number of attacks I can make per round as it does for melee combat?

Please note that this question is only about ranged attacks, not melee. I am aware of the Multiweapon Fighting feat, which doesn't actually allow you to have multiple attacks, it merely reduces the penalty for the action you are capable of by default, as noted in the "Normal: " section of the feat.

Answer 1

Normally, a creature is limited to the number of attacks it can make as per its base attack bonus plus whatever abilities give it extra attacks, and, if it has the right weapon available, the creature can use each of its attacks to make either a melee weapon attack or a ranged weapon attack.

However, an unchained summoner's eidolon is further limited in the sheer number of attacks it can make by the table Eidolon Base Statistics: The Max. Attacks column of the table

indicates the maximum number of attacks that the eidolon is allowed to possess at the given level. If the eidolon is at its maximum, it cannot take evolutions that grant additional attacks. Attacks made with weapons, including those granted by a high base attack bonus, are counted against this maximum.

Thus were the eidolon's summoner to pick for her eidolon the 2-point evolution arms and those "[a]rms… have hands, [those arms can] be used to wield weapons, if the eidolon is proficient," but simply having those arms doesn't entitle an unchained eidolon to make more attacks. The unchanined eidolon remains bound by the chart's Max. Attacks column.

In other words, if the eidolon has a high enough base attack bonus and enough extra arms with hands, all of its attacks could be attacks with appropriate ranged weapons, like a pistol or a thrown dagger or a shuriken or a crossbow wielded in one hand, but also the unchained eidolon must possess sufficient Max. Attacks as per the chart to make all of those attacks in the first place.