[RPG] How to match up an evolving eidolon with the desired look and feel

The Multi-Weapon Fighting Feat, has the answers you need.

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.

Normal: A creature without this feat takes a –6 penalty on attacks made with its primary hand and a –10 penalty on attacks made with all of its off hands. (It has one primary hand, and all the others are off hands.) See Two-Weapon Fighting.

Special: This feat replaces the Two-Weapon Fighting feat for creatures with more than two arms.

The 'normal' entry is the only place in the SRD that I can find where fighting with more than two hands and more than two weapons is covered. The Two-Weapon Fighting entry in the Combat section is short and refers only to wielding two weapons at once.

Extra attacks from BAB are not the same as extra attacks that you get from wielding a second (or third) weapon. Those apply even if you are multi-wielding (ergo, a 7th level fighter with 4 arms wielding four shortswords with the Multi-Weapon Fighting feat would have 5 attacks - 4 from multi-wielding, calculated using a base attack bonus of 7, and then another from high-BAB, on his primary hand, calculated using a base attack bonus of 2 (7 - 5)).

Notably, the eidolon's limitation on natural attacks by RAW does not apply to manufactured weapons, and natural weapons can be used as 'secondary natural attacks' (-5 to hit, 1/2 str bonus to damage) even if your main attack routine is with a manufactured weapon.

A long-running Pathfinder campaign in which I was involved that ended when characters were level 14 included—at one point or another—a half-orc inquisitor, a human barbarian, a human cleric, and a vanara druid. The campaign had the PCs as police detectives in the Magic: The Gatering setting Innistrad. Adventures involved a great deal of investigation and mundane legwork plus plenty of we've-discovered-your-evil-plot-so-it's-over! sort-of reveals in addition to beating the crap out of a lot of evil outsiders and undead.

This list is in no way comprehensive and instead limited to items I've seen used in play in an 18-month-long campaign that had a significant combat encounter only about every other session. I've further limited the list to only the items a fighter could employ.

• The half-orc inquisitor wore the bracers of the falcon's aim (4,000 gp; 1 lb.) that grants a +3 competence bonus on Perception skill checks in addition to other effects; the jingasa of the fortunate soldier (5,000 gp; 3 lbs.) which, while a combat item, I'd be remiss were I not to recommend; and the mushroom vest (500 gp; 3 lbs.) that lets the wearer treat falls as 20 ft. shorter, which, admittedly, isn't the boots of the cat (1,000 gp; 1 lb.), but the boots slot is premium real estate in Pathfinder. When needed, he'd doff the vest and don a robe of infinite twine (1,000 gp; 1 lb.). I'm pretty sure he also wore the heavyload belt (2,000 gp; 3 lbs.) and the muleback cords (1,000 gp; 0.25 lb.) so that the weight he could lift, drag, or push was measured in tons. At later levels, he discovered the gloves of reconnaissance (2,000 gp; 0 lbs.) and cried a little, regretting he'd not been wearing them all along, then never took them off.
• The human barbarian with the drunken rager archetype had several utility magic items so that, despite not casting spells, he could feel useful during investigative portions of the session. These included the cloak of the hedge wizard (transmutation) (2,500 gp; 1 lb.) that cost 50% more because it was combined with his cloak of resistance +3 (4,500 gp; 1 lb.), a wayfinder (500 gp; 0 lbs.) with an ioun stone (clear spindle) (4,000 gp; 0 lbs.) so that together they resonated with an immunity to mental control as per the spell protection from evil, the ioun stone (eastern star) (4,000 gp; 0 lbs.) so as to be able to read and understand all languages, the noble's vigilant pillbox (3,600 gp; 0 lbs.) because of its detection abilities, the ring of the sophisticate (11,000 gp; 0 lbs.) so he could find a bar anywhere, and, later in the game, the expensive drinking horn of bottomless valor (24,000 gp; 2 lbs.) that was useful also as a source of endless booze so as to freely liquor up suspects and witnesses to get them to talk.¹
• The human cleric's player's first big purchase for any of his characters is almost always the hat of disguise (1,800 gp; 0 lbs.), which is probably near the top of almost anybody's Versatile Magic Items list. Looking back, I would suggest now that he buy first—and later pay the extra 50% to combine the hat with—a cap of human guise (800 gp; 0 lbs.) because it's cool, too.
• The vanara druid's elephant animal companion wore a belt of the weasel (10,000 gp; 1 lb.) so that the elephant could more easily enter people's homes during investigations. (Shockingly, folks were still uncomfortable having an elephant in their homes.) However, the party soon realized the belt's utility value, and the belt ended up as often on a party member as the elephant. If the belt seems overpriced, then reread the universal monster ability compression that the belt also grants: it's awesome ("You can squeeze through a space how little exactly?"). The vanara druid herself wore a ring of eloquence (3,500 gp; 0 lbs.) but custom made so as to include, instead of its typical languages, the four elemental languages so that she could communicate with her summoned allies.

In retrospect, we weren't using several items that we probably should've been using. In addition to several ioun stones (cracked orange prism) (1,000 gp; 0 lbs.) each for the casters because more 0-level spells is incredible, I'd want now, for instance, the headband of intuition (7,000 gp; 1 lb.), at least one insistent doorknocker² (5,000 gp; 2 lbs.), and the treasure hunter's goggles (6,400 gp; 0 lbs.).

¹ The drinking horn supplemented his low-level purchase, the tengu drinking jug (1,000 gp; 2 lbs.). He'd tired of the one gallon of sake or plum liquor ("Tastes like pruno") the jug could create each day, even though it was sort of free.
² Two doorknockers are better so that you can make a door then make another door on the other side to recover the first doorknocker, but even just one's great for a case of the lookarounds.