Thanks for the additional information. I really appreciate it.
Although a power struggle over who is dominant can result in interdog fights in a home, there are also many other possible causes that range from fear and anxiety to hormonal issues.
There's a good site that discusses interdog aggression here:
That being said, the first step is to have the aggressor of the majority of the fights seen by the vet to rule out possible medical reasons for the fighting. Things like thyroid issues can cause behavioral changes (usually to the aggressive) in dogs. Having your vet take a quick peek and run a thyroid test and/or any other tests they think could explain this behavior is the first step. I know that he's already seen the vet, and is on some medication, but I'm not sure if they did blood work, so I wanted to mention it, just to be on the safe side.
If that comes back clean, then you'll have to figure out how to handle this situation. Make sure you don't ever yell or physically discipline the dogs when they're fighting. Raising your voice causes the excitement in the dogs to increase, which can make them fight even more. Also, using physical punishment will only make them feel like they really do have something to be worried or afraid of. When they start fighting, the best thing to do is to quietly and calmly separate them if possible. Sometimes allowing all the dogs to have leashes on while in the house will give you something to grab and use to pull them apart so that you don't get bit accidentally.
If you're reluctant to do that, then you're going to have to take steps to ensure that the aggressor isn't ever left alone with the other dog. Since one dog is already crate trained, it might not be a bad idea to use a crate with Neo as well. Crates/Kennels provide a safe place for a dog to retreat to when they're overwhelmed about something. Additionally, getting everyone crate trained will make it much easier to control who is out interacting with each other.
You should also feed them in the crates and make sure to separate them when letting them outside.
Unfortunately, if you're unable to get these ideas to work, you may have to consider finding a new home for one of the dogs. It's definitely possible that your aggressive dog simply can't live peacefully with other dogs. It's actually pretty common to have dogs who have lived together fine before develop aggression as they age, so if your more aggressive dog can't live happily in your home, the finding him a new place may be the best not only for him, but for the other dog (and you!) too.
I hope this helps.