I'm running my players through Skull & Shackles 2 - Raiders of the Fever Sea atm. My pirate captain player acquired the parrot Rotgut as his pet.
He asked "If I attempt to Intimidate and Rotgut mimics a part of what I threaten with. Would I gain a small Circumstance bonus with that? As small as a +1 or even a +1/2 (If we tie I still win). Examples being "You look like you can fit in my Deathsack". "Awk! Deathsack". or "I'm going to start sawing off your fingers if you don't tell me where the treasure is". "Awk! Saw his fingers off"."
What are your thoughts about giving him the bonus? would it be overpowered?
A +1 circumstance bonus wouldn't be overpowered IMHO, especially if he has to make a Handle Animal check to get the parrot to DTRT.
(I'm less sure that it's justified, personally I don't think I would be [extra-]intimidated by the parrot.)
Aid Another
In melee combat, you can help a friend attack or defend by distracting or interfering with an opponent. If you’re in position to make a melee attack on an opponent that is engaging a friend in melee combat, you can attempt to aid your friend as a standard action. You make an attack roll against AC 10. If you succeed, your friend gains either a +2 bonus on his next attack roll against that opponent or a +2 bonus to AC against that opponent’s next attack (your choice), as long as that attack comes before the beginning of your next turn. Multiple characters can aid the same friend, and similar bonuses stack.
You can also use this standard action to help a friend in other ways, such as when he is affected by a spell, or to assist another character’s skill check.
Technically if it has any kind of intelligence, it can AID another intimidate vs a 10, and if it succeeds it adds a +2 to your own check. If it fails, it has wasted an action.