Before I begin, just let me say dogs are kind of my "thing". I'm part of several dog forums, have been active in dog rescue for the past 15 years, and had read several books on canine psychology and behavior in my spare time. So, I'm not just talking out of my ass here.
Here's a fun but little known fact: there is no such thing as "alpha dogs" or dominance in dogs as we think. Infact, the scientist who coined the term "alpha" made a statement a while back that he regrets it. The study that made the foundation of canine behavior as we know it today is extremely out dated. It was based on a wolf study done during the 1940's where scientists took a bunch of random adult wolves that didn't know each other and stuck them in a pen together to be observed. The wolf that laid claim over the natural resources in the small area was considered the "alpha". The truth is, in the wild, wolves act VERY different. Packs are in actuality family units. The "alpha" male and female are the breeding pair, or the parents, and the "pack" are their offspring (their pups), who once they reach sexual maturity around the age of 2 or 3, go off on their own to find their own mates and start their own "packs". So in other words, ALL wolves become "alphas" at some point.
If dogs are indeed descendants of wolves (which is debated these days too, but that's another topic), it's a similar concept. Their social structure isn't as complicated as people once believed. They are a social species, yes, but there is no "trying to dominate other dogs to be pack alpha". With my dogs, you'll see Ma'ii, my Blue Heeler has possession over the bed. If Charlotte approaches and tries to lay down, he'll growl and snap at her and she'll turn, avoiding eye contact, and walk away. It would have been believed that Ma'ii is the "alpha" and was displaying dominance over Charlotte. However, if Ma'ii even THINKS about touching Charlotte's toys, it's all over, and he knows it! Charlotte will give him a red ass beat down. As we've moved and our living situations and surroundings have changed, so has our dogs claims over resources. In our old place, Charlotte had claim to the bed and would growl at Ma'ii if he tried to jump up. So who's the dominant one? Neither. They are equals, it's just one has claimed one resource over the other. Also, they aren't a pack. They are friends, they like each other and play together, and will even stick up for each other if another dog threatens one of them, but if anything ever happened to my husband or I and they were left to their own devices, they'd probably separate and go their own ways. They'd probably hang out on occasion, but they wouldn't actually live together.
So, back to the topic at hand. There could be a number of reasons as to what's making your dog act like a jerk. You mentioned he's a Pit mix. Dog aggression is extremely common in that breed once they hit sexual maturity, even if the dog is mixed with something else and especially if he's still intact (please note though that dog aggression is NOT the same thing as human aggression, and should NEVER be thought of or treated as such). If that's what the problem is, there isn't anything you can do to train it out of him, because the problem is genetic rather then behavioral, and due to a high prey drive. Getting him fixed might help a little, but it won't solve the problem. When introducing him to other dogs, make sure he's leashed and become familiar in canine body language. Charlotte, who is a Pit mix too, can be extremely aggressive with strange dogs, so I learned to read her. I can tell just by looking at the dog before she even sees it, as to weather or not she's going to be okay with them.
That's if DA is even the problem. It's hard to tell without actually seeing him myself. It could be something else, or it could be a combination of problems. Some dogs are just bullies, just like some people are.
