That's pretty much my question: The Response effect says "After Brand son of Bain attacks and defeats an enemy engaged with another player,...", and that seems to me to include attacks in which Brand is joining his Ranged attack to other attacks to defeat an enemy. But sometimes the rules do strange things, so I thought I should check. If it is as I expect, that's really cool since Brand could combine with Gimli, controlled by a second player/deck to attack an enemy engaged with that player/deck, and then Gimli can be readied again for a second attack.

~Bene

There is nothing that says he must attack alone in there. If it was supposed to be by himself it would have to specify.

Svenn is correct. From p.7 of the latest FAQ:

"Q: Can Brand son of Bain (SoM 72) trigger his response if he participates in a ranged attack that defeats an enemy engaged with another player instead of declaring the attack himself ?
A: Yes. Declaring an attack and participating in an attack are both subsets of attacking. In both cases Brand attacks and can trigger his response if the enemy is defeated."

From this, two important points are clear:

1. Brand does not need to attack alone (he can trigger his effect while "participating" in an attack).

2. The attack in which he participates can be initiated by any player.

So, if an allied Gimli were to attack an enemy, Brand could definitely chip in. Should the foe be destroyed, Brand could ready Gimli and allow the dwarf to murderize another hapless Orc. There are a bunch of neat little tricks you can pull of with Brand--he works extremely well with Beravor, for instance.