If you could turn invisible afterwards (ideally as a move or swift action in the same round) they'd be denied their dex bonus against you for the invisibility duration. Similarly if you have a means of hiding, in plain sight or otherwise, or could blind them.
The duration of the actual feint can't be extended except by feinting the enemy again though.
For low to mid-level PCs, I came to the conclusion (rightly or wrongly) that Dirty Trick is hands-down superior to feinting in combat. Perhaps with the exception of adversaries who have a high DEX bonus to AC. There just seems to be more things you can do to boost your Dirty Trick attempt than with feinting.
Tell me I'm wrong. <g>
It's easier to send a skill bonus through the roof than a CMB. Successful feinting is...easy. Even with a -4 or -8 on it, once you have a few levels.
With Greater feint, the duration of the denied-dex effect lasts until the end of your next turn. Is there any way to improve that?
Repeatedly delaying your turn?
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For low to mid-level PCs, I came to the conclusion (rightly or wrongly) that Dirty Trick is hands-down superior to feinting in combat. Perhaps with the exception of adversaries who have a high DEX bonus to AC. There just seems to be more things you can do to boost your Dirty Trick attempt than with feinting.
Tell me I'm wrong. <g>
Feinting has a lot of problems, the biggest being action economy. You need at least three feats to make it as part of your full-attacks, and to get the benefit for more than one attack. So it's definitely a mid-to-high level option. Dirty Trick is basically in the same position at the early levels, unless you've got class-specific buffs to prevent the maneuver from eating up your standard action each round.
Why Feinting is ever considered an option is because it's easier to raise your skill bonus than CMB, especially for 3/4 BAB classes. But since targeting flat-footed AC is usually worth +3 to Attack, you shouldn't bother unless you've got rider effects like SA.
We could morph the thread into discussing those builds, but I first have a second question:
can the Seduction inquisition be activated any time I feint (as a move, swift, or ability-triggered action), or only when I use a standard action?
Standard action. It doesn't modify your feint attempts, rather it just functions as a feint in combat. It would also provoke AoOs.
It would provoke AoO? That's disappointing, why?
It's a spell-like ability, and those provoke. I think you can make a concentration check to cast it defensively, with a DC of 17 since it's considered a 1st level spell.