Quote Originally Posted by The Giant

Yes, but in the case of a monster with two Support abilities, they are considered separately. So you could negate Horde or Assist, but not both. This is, incidentally, one of the best uses of this particular card and can be essential in breaking up very powerful clumps of monsters.
Yep... especially since, if I read Horde correctly, it can lead to some large stacks. For example, a monster with Support:Goblin/Horde could theoretically have every Goblin in the deck stacked under him.

Another question: Monsters with the Flying ability can only be battled with a Shtick with Range > 0. Now, if the player is in the same room with the Flying monster, is it still considered a Range 0 attack for other purposes? (example: Can Haley Sneak Attack flying monsters?)