How does this work? Specifically does it allow you to respond multiple times?

Eastwatch-by-the-Sea (1)
[baratheon Location]
The North.
Response: After an opponent reveals a plot card, move 1 power from a character in play to its controller's House card.

I assume the ruling is consistent with these cards too (assuming something affects multiple cards at once)

Joffrey Baratheon (3) (3)
[Lannister Character]
Lord.
Immune to triggered effects.
Response: After an opponent's character is knelt, pay 1 gold to stand Joffrey Baratheon. Then, he claims 1 power.

Anguy the Archer (3) (3)
[Neutral Character]
Brotherhood.
Deadly.
If you have no power on your House card, Anguy the Archer gains: "Response: After an opponent's character is killed, Anguy the Archer claims 1 power (limit 3 per phase)."

Yes to all three examples. However, you need to be able to kneel Joffrey as a Response effect while the action window is still open (you can trigger Joffrey's ability for each knelt character controlled by an opponent, but he needs to be able to go from kneeling to standing each time in order to gain the power). Seeing as to how he is Immune to triggered effects, you will need to be able to blank that first.

the1andonlime said:

Important point, though. The "stand, then claim power" nature of the effect creates a limitation on the effect. The first part (standing) must be successful before the second part (claiming power) can be successful because of the word "then." So even though you can technically trigger him for each knelt character, it isn't necessarily going to do you any good.

ktom said:

You could use Den of Wolves to make Joff lose his Immunity. That would keep his Response intact.

the1andonlime said:

True, but then you aren't blanking him, right?

ktom said:

Aye!