We just added Max, a treeing walker hound, to our family in january. He's around 3 and came from the SPCA, so, like many shelter dogs, he has some alpha issues. He had lived with cats previously, and he likes Sammy and Lola, though they don't cuddle together or anything.....but will sleep separately on the same surface such as a corner of the carpet, or the sofa. He has definitely taken over top spot of the three animals, due to both his size (70lbs) and personality. He and Sammy get along pretty much full time, but Max doesn't always think Lola should leave the bedroom (her "home" while they were still separated). We've been working on this issue and progress is being made. He'll now only chase her back to her room some of the time, which is an improvement. Also, he is now spending some time in the bedroom with Lola, which is helping her relax around him and helping him get used to seeing her normal behaviours, which we're hoping with contribute to his acceptance of her throughout the apartment. We have socialized them to the point where they can basically be around each other with no problems unless there is human food involved.....if we're eating and Sam is closer to us than Max is, Max sometimes might get a little upset about it, even though neither of them is getting any of our food. We find that repeating "no food, Sammy" helps Max realize that we're not giving Sam anything (it's amazing how fast Max learned Sammy's name). But other than that specific situation, they're cool.
Max IS a hound and he likes to dominate by size and chasing, running past Sammy or straight at him....but when he gets up to Sammy, he's only interested in sniffing or flopping onto the ground for a rest lol. Sammy has clued into this and doesn't run anymore, which solves a lot of the chasing problem. We're still working on the "no-chase" command, but, as with many shelter dogs, we'll have to be patient and dedicated before all is "perfect" (or close enough).
I should mention that hounds are not always good with smaller animals like cats, and that we were aware of the work ahead of us when we added Max to our furry gang. But so far, he's been a great addition, fitting into our lives very nicely. It looks like, with some time and commitment, we'll all be living happily ever after