I partially work with dog sitting and have a little pack of a handful dogs that I take care of a couple of days a week (that is, typically I have each dog 2-3 days per week, sometimes they are alone with me, sometimes I have a couple of them, but I have limited it to 3 simultaneous dogs because more than that is impractical when I take them for a walk).
One of these dogs is a 4-5 year old neutered male shelter dog that very much looks and behaves like a jack russel terrier. Let's call him B.
B was the second dog I started to take care of, before him I had A, a eurasian bitch that I have had since she was 4,5 month old (A is now 1.5 years old).
Unsurprisingly A was submissive to B and everything was fine (A is very submissive when meeting dogs in the dog park, spending most of her time on the back, never causing any troubles). After a couple of month A and B had a one or two fights, nothing serious (i.e., no blood or so but some growling, baring the teeth and some attempted bites). Suddenly A was dominant and B was submissive to A.
After these incidents, B suddenly become very affectionate towards me and my girlfriend. Sometimes we deliver B to his owner somewhere outside (rather than she comes by here and pick him up which is the normal procedure) and he always refuse to walk away with his owner on these occasions and show all signs of unhappiness when I leave (he is very happy to see his owner, it is just that he can't bear that I leave).
After a while I also got a male pomeranian, C, that is of approximately the same age as B. Still no problem. C is quite reserved and doesn't care about me nor other dogs. C is chemically neutered. Only time he shows happiness is when he is picked up by his owners in the afternoons. Still no problems. A, B and C get along well as long as I serve them their food a bit apart.
However, recently I got two more dogs, a male shiba puppy, 4-5 months old, D, as well as a female dachshund, 1,5 years old, E.
Now the problem started: D and E are submissive to B but he is not satisfied with that and harasses them so much that they are scared of both him as well as going through my door when their owners leave them in the morning. Especially D suffers from severe bullying by B and B frequently snap at him, which, not all the time but at least once a day, makes D scream and show all signs of being very scared (shivering, hiding in a corner near the door, focusing all his attention on B and so on).
So far, B has not (AFAIK) "punched hole" in D's skin when he has snapped him. Of course we have examined D after these attacks but "squeezing" D, moving his joints, examining face and ears and similar has never revealed any wounds or painful spots, although he has been limping for a short while once or twice after such an incidents.
Of course, I roar at B immediately after every incident which makes him roll over on his back, avoiding eye contact with me and show all signs of being submissive.
Generally B has no problems with other dogs when we are in the dog park. He doesn't play that much with other dogs but when other dogs run around in groups he kind of herd them by running behind, barking and trying to snap their hocks (but there has never been any incidents where he has injured the playing dogs he chases like this).
However, during the year I have had B has three times bitten humans. Twice men in their 60s, once an lady in her 80s. B's owner says he has a problem with slightly overweight men in their 60s and both of the male victims above matched that description. Remember, B is a shelter dog. It wouldn't be surprising if he has been abused by men matching that profile.
All these three attacks has been at the heels or calfs. Twice the person wore jeans, once the victim had bare legs. The bite didn't punch hole in the jeans and the man with bare legs only got a very shallow scratch on his skin (like you can do on yourself with your nails). Of course, biting humans, even though the bite is not very severe, is not acceptable behaviour from a dog but he doesn't seem to bite to injure the victim. However, these attacks has all completely unexpected. We have been walking down a crowded road and he just ignores everyone we meet until he suddenly attacks (we frequently go by public transport and he has no problem with that, he mostly sits or lays around my feet ignoring everyone around).
Furthermore, B's owner told me, after I told her about the first incident with D, that B doesn't like puppies. But obviously all puppies are not a problem - A was a puppy when they first met and B has no problems with most puppies in the dog park.
When it comes to E, B is not physical towards her, he just dominates her and forces her out of his way into a corner somewhere. When I have B, D and E together, unless I intervene, D and E end up in a corner near the door clearly very tensed and nervous.
I have tried going out somewhere where we are alone in the nature and release them all together to give them plenty of time and space to figure out their hierarchy but nothing "happens": B just hangs out quite close to me waiting for us to be "done" while D and E take the chance to sniff around and play with each other.
So what is behind B's aggressive behaviour towards D and E? And how can I make them get along?
Response to @Elmy's very well written comment:
Thank you for your views. Especially the first one made sense. We had kind of interpreted the situation as B, when A raised in the hierarchy, wanted to be "on good footing" with us since he was lowest in the rank. Does that make sense? If B is below A we thought he felt us humans could protect him from A if the need arose and to achieve that he become affectionate towards us.
Anyway, yes he probably guards and protect us when around other dogs. But, when we are in a dog park, he is not as close as you suggest: typically he is a few meters away but he is very attentive to when we are about to leave and immediately follow us when we start moving. He clearly does not want to be left alone (maybe due to his life in a shelter). The other dogs act more "natural" here and want to stay and have fun and therefore have to be called in.
Can you elaborate on how I tell him to stay behind [me]? Do you mean when he is on leach or when he is off leach?
Of course I don't justify his biting, especially not when he attacks humans  . However, the shelter dog information seemed important to include when analyzing the situation. A dog that has always been treated good and bites is different from a dog that has been abused and bites.
What do you mean by "too late"? My reaction is within a few seconds, the attack might still be ongoing when I react. However, I don't spend my days watching every step my dogs take so, unless I provoke an attack, it would be sheer luck if I could see it beforehand. Your suggestion seems unrealistic.
That doesn't mean being mean to any dog and constantly putting them on their back. It means setting the rules and controlling that everyone followes the rules. Make it a rule that noone is allowed to overly dominate someone else.
How do I achieve this? When B is with A and C he is very nice and calm, both to them and to me and has no problems if I play with A and C or they are in my knee, I serve them food or something. And B is still very nice towards me when D and E are around so I am not sure how I can construct a situation where B and I would have a "dominance competition". The only thing I can imagine is if I play with B and give him something to pull and drag. I always end these games by "winning" and taking the toy.
Regarding the last advice: yes, I always "double" the leach (= the length is halved) when walking around among people but sometimes unexpected things happens (The last attack on a human happened when we had been swimming from some rocks. I had him in his leach when we climbed out of the water on some slippery rocks but fell and lost the leach.).
 In between dogs some biting is acceptable, isn't it? The other dogs in my pack sometimes tumbles around playing and everyone is content and happy. Afterwards you can see that they are all greasy around the neck from "soft" bites in each other furs. One of them is white and has "flappy" ears and from time to time you can even see a small pink "stains" in his fur on the ears, probably a minuscule amount of blood when someone by mistake scratched him a little too hard. I have never heard him scream or anything like that so I guess it is just accidents that doesn't bother him that much. Anyway, this has nothing to do with B.