Depends on the needs of the first dog. Is it needy, how old is it, how much time do you spend with it, etc?
My girlfriends dog is the biggest PITA I've ever seen...acts like he hasn't seen her in years, when she's only been gone a few min...knocking stuff off the tables, scratching people, jumping on her, etc.
We got a Pit puppy about a month ago. Every time she shows attention to the Pit, her dog starts a fight, because he's jealous and possessive.