Getting the most out of a big pile of attacks

[Extra Anchovies]

Eleven attacks, to be exact. Four from BAB, three from TWF, and four natural (secondary). For context, I'm going to be playing an Aegis (http://www.d20pfsrd.com/psionics-unleashed/classes/aegis) with the Aberrant (http://www.d20pfsrd.com/psionics-unleashed/classes/aegis/archetypes/dreamscarred-press/aberrant) archetype, and will be heavily Dex-focused (Weapon Finesse, Deadly Agility, and Piranha Strike, in addition to Multiattack and the core TWF chain). Besides Hammer the Gap, what other feats are good for taking advantage of the pile of attacks I have available?

[Abd al-Azrad]

Awesome.

I'd basically say anything that can add a damage boost of any sort, at this point. Arcane Strike would be beyond ideal, but of course you need an SLA (racial if possible). Critical feats like Staggering and Stunning Critical might not be a bad investment - your threat range may be low, but with four tentacles or seven weapon strikes, that's a lot of chances to roll high every round.

A weird idea: Desperate Battler (http://www.d20pfsrd.com/feats/combat-feats/desperate-battler) gives you a mediocre +1 morale bonus to hit and damage when your allies are 10' or more away. Not great on its own, but with a +4 Courageous weapon (in your off-hand possibly) or a +2 Furious Courageous one and a method to enter Rage, your morale bonuses would increase by +2 each - and +3 to hit and damage really doesn't suck with 11 attacks.

In general, I think when you're firing off that many attacks a round, your focus should be on making sure you can always full attack. Pounce by some method, or Antagonize (even the crappy debuffed version) can make sure your enemies are as close to you as possible. Damage reduction will also be an issue for you, which you can't really solve with feats alone (Eldritch Claws only delays the problem a bit) - for that, you'll need alchemical weapon blanches and, inevitably, a really expensive Amulet of Mighty Fists.

EDIT: Have you considered Precise Strike (http://www.d20pfsrd.com/feats/combat-feats/precise-strike-combat-teamwork)? It will be VERY difficult to use at the same time as the Desperate Battler trick, but if you can manage Reach with your Aegis buffs (which you can), you might be able to flank and keep your allies 10' or more away. Also, pick up Powerful Build with your Aegis customization points if you can, it's free damage.

[stack]

Brutal disruptor cryptic after you get your tentacles to add disrupt pattern to every hit.

Grab akashic veils that boost damage (forcestrike knuckles for starters).

PoW stances. I believe Primal Fury has some per hit damage boosts.

[Abd al-Azrad]

It's a bit of a feat investment (Blind Fight and Combat Expertise, plus racial requirements) but Moonlight Stalker (http://www.d20pfsrd.com/feats/combat-feats/moonlight-stalker-combat) can give you a nice +2 to hit and damage against foes from whom you have concealment. Plus the prerequisites are pretty decent feats.

[Extra Anchovies]

EDIT: Have you considered Precise Strike (http://www.d20pfsrd.com/feats/combat-feats/precise-strike-combat-teamwork)? It will be VERY difficult to use at the same time as the Desperate Battler trick, but if you can manage Reach with your Aegis buffs (which you can), you might be able to flank and keep your allies 10' or more away. Also, pick up Powerful Build with your Aegis customization points if you can, it's free damage.

Hm. Precise Strike I like, +3.5 average damage/hit is nice. I do plan on taking the Reach customization, and eventually Size Increase as well. I don't think Powerful Build boosts natural weapons, however.

Arcane Strike is not one I had thought of, but would be very potent. The Aberrant gives Vim at-will as a Psi-like, would that qualify? And if not, is there any easy way to get ahold of a racial SLA while also getting a bonus feat at 1st (maybe some alternate human racial trait)? With the TWF chain and no class-granted bonus feats, this is going to be a bit feat-intensive.

[CGNefarious]

I'm pretty sure there are some traits that can give you a limited use SLA.

[Abd al-Azrad]

As a DM I wouldn't let Psi-like abilities work to trigger Arcane Strike, but that's only because I am a severely persnickety DM.

First trait I've seen in the list is Chosen One (http://www.d20pfsrd.com/traits/faith-traits/chosen-one-faith), which gives you Light 1/day at CL = your level. Indeed, all SLAs use your total HD as their CL, so it doesn't matter which one you select. However, do feel free to look around for better ones. One gives you your choice of 1st-level domain spell, which is nuts.

[deuxhero]

A shame PF nerfed completely changed Wounding, because that would be a good option.

Only source of rider effect ability damage I know in PF is 2 levels of Ninja/Rogue for Pressure Points or a lot more levels of one of those (or Vivisectionist Alchemist) for Crippling Strike