I have a question about the black dog and how it interacts with the negotium conspiracy. If a 3 cost character or higher commits to another story can the black dog use his effect and go to that story since its a response or will he not be able to since he costs 2?

I think the Black Dog can. Negotium disables committing to other stories. But Black Dog comes into play in the state of being committed to a story. This does not count as committing, so you can use the Black Dog.

(If you're interested in the reason: There's a difference between the character state of "committed" (and "uncommitted"), and the act of "to commit" (or "to uncommit"). You do commit characters to stories in one of the first green boxes in the story phase on p. 13 of the rules, and this automatically includes the change of the state of your characters from uncommitted to committed. But there are other ways of getting into the committed state which do not count as "committing a character" (the effect of Black Dogs for instance), and there are other ways out of the committed state than the usual uncommitting at the end of the story phase (e.g. a character being killed because of a combat struggle makes him go to the discard pile).)

 +1 for Black dog response laughing at negotium and doing its thing.

yes it can. been discussed and approved. so black dog away !!