Short Version: Anyone can manifest 1 extra pair of arms with the power. Getting another pair requires a moderate investment in ego and a few character levels. Toughness helps a little too.
Getting your third pair requires a high level character with a huge investment in ego. Costs scale up heavily with each new pair.

Intro
I'm not the creator, just a fan of the mod. This little guide should help you build better characters with psybrachiomancy.
Here's my findings after looking through the code and doing some basic testing. Thanks to Winged Monotone for the great mod. Also thanks to them for giving some advice on my (now defunct) Scrapbot AB-I mod a few years ago. If they have any objections or corrections, I'd be happy to change what I've done here.


Math and Arms
Psybrachiomancy tests against your maximum psi charges to determine how many times you can manifest an additional pair of arms. In game testing got me these numbers.
Number of Extra Pairs:Max Psi Charges Required
1:0
2:6
3:24

Or, to translate that to a level 1 character (with 18 toughness),
Number of Extra Pairs:Ego Required
1: 0
2: 24
3: 56

I didn't test further, because getting the 56 ego for the third pair of arms is already well beyond what most players will achieve. The only character I would estimate to get 3 or more extra pairs of arms would be high level ego-centric characters.

Your max psi charges should equal
Ego modifier + (.5 * Toughness modifier) + (character level * ego bonus * .1)
Willpower affects psi recharge rate, but does not affect max psi charges. So it has no effect on psybrachiomancy. There's also a debuff if you try to manifest more arm pairs than your willpower modifier, but it is temporary and easily ignored. It likely only has an effect if you need to manifest an arm after losing it in combat.

One thing I can't easily test for is character levels and how they affect max psi charges gained. At a glance, it looks like you add your ego modifier to psi charges once every ten levels.
So an ego 30 (+7 modifier) esper, at level 20, would have a max psi of about 22. Sorry I can't be more precise. There's too many moving parts, considering toughness gain and other factors. Also it calculates per level, but I simplify to per 10 levels.


Build Advice
Esper: It could be a solid mutation if you want to be able to hold and wear more items.
Akimbo Gunslinger: The new arms DO grant missile weapon slots, so this is a strong contender to replace or supplement Many Arms or Chimera. Though it would require a big investment in ego and probably waiting a few levels for the second extra pair.
Melee Dual Wield: I don't see much synergy here, since your penetration stat would be strength for your default fleshy arms, but ego for your psychic arms. MAD (multiple attribute distribution) problems. Though I suppose anyone could benefit from a few extra slots.