Sons of Eärendil has text which reads:

Response: After another player raises his threat, raise your threat by 1 and reduce that player's threat by one.

Would this mean that, (in a 4 player game), if all players were forced to increase their threat, the player with this card can reduce all other players threat by 1 and increase their own threat by 3? I don't see any restrictions for the number of times this can be done.

Yes, sounds right to me.

edit: and further, since Song of Earendil is not a unique card, you could play 3 on a single hero.  In a 4 player game, if you lost the Questing phase, you could then use that to reduce every other player"s threat by 3 and raise your own by 9, if you had a mind to do so.

Based on errata and timing of "response" effects, anything which triggers more than one response simultaneously can only happen once, not multiple times. So in this case, if a card/effect raises each players threat by 1 (simultaneous effect) the Song card can only be used on one of the four players.

Highland Shade said:

Hmm…

Here's that part of the FAQ:

(1.08) Responses per Trigger

If a response or forced response is triggered, the effect can only occur once per trigger.

Example: Theodred (CORE 2) reads, "Response: After Theodred commits to a quest…." This effect can only be triggered once each time Theodred commits to a quest.  (p. 4)

This would clearly mean that one response can be used once per trigger.  So, if you have 1 Song of Earendil, you can only trigger the response one time by that card (you can't use that one trigger to continually activate the Song's response text).  As I am reading it, though, this text doesn't address multiple copies of a card, or multiple responses being activated off of a single trigger.  So three copies of Song of Earendil should be able to activate their response from a single trigger (but only one time each, as per the Theodred example above).  Or, for example, if a character leaves play, you may trigger the Horn of Gondor's response AND Prince Imrahil's response AND the response on Misty Mountain Eagles.

In that response above I lost sight of the original question, so I wanted to add also that if three characters leave play, that's three discrete triggers and one could trigger the Horn of Gondor's response 3 times.  Likewise if three different players raise their threat, a single copy of Song of Earandil should be able to be triggered 3 times.