Outside of combat reflexes or other things to give you more, you have one AoO per turn. Provoking an AoO and having an AoO available to swing are two different things. Just because an opponent provoked doesn't give you more AoOs.
If you have all the feats you mentioned above, and you and your allies always confirmed your critical hits, you would indeed to chain provocations and you would get attacks of opportunity up to the point that your dexterity bonus allows.
Grab Broken Wing Gambit and you wouldn't even need to confirm criticals for chain AoO provocation fun and games.
Well, if all 3 of your allies have Broken Wing gambit and use it on thier attacks of opportunity, not only would you gain attacks of opportunity from your own and allies crits, you would gain attacks of opportunity from your enemies attacks as well.
Especially if you use something like Great Cleave and reach weapons.
Every time any 1 member of the trio score a crit, all 3 players will get to make an extra attack. This continues until they are out of AoO as per combat reflex and other sources.
This 4 feat combo (less if one has the ability to grant teamwork feats) can include any number of players, so long as they threaten the target.
On top of all that, the FIRST crit is at a +4 to the attack, and all subsequent attack triggered are at +8.
Slap a Menacing weapon in any of the members hands, those numbers become +6/+10.
Best 3 musketeer build ive seen yet.
This somewhat depends on how you interpret the no more than one AoO per trigger rule. Conservative readings of that rule prevent teamwork feat AoO chains. Since all subsequent crits are the results of the originating crit for which you have already taken an AoO, you cant take any more as a chain.
The no more than 1 AoO rule is saying a situation were player A and player B are both flanking a target. The enemy Goblin decides to make a break for it, and in his movement, provokes from both players. Now since player A triggered an AoO, the feat grants one to player B, and vice versa, However this AoO is triggered by the movement, so no matter what they only get 1 AoO from this movement, either the one granted naturally, OR the one granted from the feat, but not both.
However in this crit chaining:
-Player A uses a standard action attack and lands a crit.
-Player B triggers an AoO(1) via Outflank.
-Player A triggers an AoO(1) via paired opportunist.
-Player A Resolved his original attack.
-Player B now takes his AoO(1), and scores a crit.
-Player A triggers an AoO(2) via outflank for the first time, independent of his original standard action attack.
-Player B triggers an AoO(2) via paired opportunist for the 2nd time, but from a different attack source.
-Player B resolves his first AoO(1).
-Player A now takes his first AoO(1), for simplicity we will end the crits here.
-Player A resolves his AoO(1)
-Player B now takes his second AoO(2), again, no crits.
-Player B resolves his AoO(2).
-Player A now takes his 2nd AoO(2), again no crit.
-Player B resolves his AoO(2).
The chain now ends, with each player landing 1 crit each, granting player A 3 attacks, and player B 2 attacks. If any more attacks land a crit during the chain, it again grants each player an additional attack, via the two feats.
I have a build based on this. 3 levels of Hunter, and instead of Gang Up, I have Pack Flanking. I, a goblin, ride my animal, and have Animal Ally to continue it's usefulness. Dex build, two-weapon fighting, and combat reflexes, so lots of AoO's with a high crit weapon.
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The usual interpretation I have seen is that the 'one AoO per trigger' applies to the original triggering event which set off the chain. Otherwise, Paired Opportunist alone leads to AoO chains being capped only by Dexterity bonus;
AB
1
Characters A & B both threaten enemy 1. If enemy 1 does something that provokes an AoO from A then B also gets an AoO due to Paired Opportunist... since B just got an AoO A does also due to Paired Oppurtunist... so B gets an AoO also... so A gets another AoO... and so on ad infinitum.
This is the same logic being applied with the Outflank chaining based on crits. However, that seems very unlikely to be the intent IMO.
Rather, in the example above the chain would stop once A & B had each gotten one AoO... because there was only one triggering event.
Likewise, with the Outflank crit chaining... replace Paired Oppurtunist with Outflank and in the example above have the A&B flanking 1 and each character getting a crit on every attack... per the interpretation presented in this thread they would keep generating AoOs for each other until they ran out of AoOs for the round. However, per the one AoO per triggering event rule the chain would end once each of them had gotten a single AoO off the original triggering critical.
Paired Opportunist reads "ENEMIES THAT PROVOKE attacks of opportunity from your ally also provoke attacks of opportunity from you..." [my emphasis]
Outflanks reads: "whenever you score a critical hit against the flanked creature, IT PROVOKES an attack of opportunity from your ally" [my emphasis]
As I read that, an outflank critical doesn't trigger paired opportunist since "it" (you scoring a critical hit, your action) not an "enemy" (enemy action) provokes the attack of opportunity.
Add this to my agreement with the "one trigger' interpretation to break the very silly chains of extra attacks.