i used to run a small animal rescue centre here at my farm,, when i say small..lol.. i had 336 animals . mostly farm and wild animals but i had some unwanted pets also.. we never used to take rescue dogs in though so im not sure this advice would be suitable but it worked with cats so why not give it a go.

this will only work if your other dogs are not really used to your car though!

get all of your dogs and put them in your car and drive around for an hour or so (if they will all fit in your car) they get a bit scared and are sort of thrown together and end up best of friends..it works for cats a treat..( but of course the cats wouldnt be free in your car..they should be in the largest box you can get your hands on)

i suppose you could maybe do the same sort of thing without a car..put them somewhere they are not used to and even maybe with a stranger present.. maybe in someones (a friend) garage. leave them there for an hr or so..but of course stay close at hand and go and check them often. they will be so pre occupied with there new surroundings that they wont notice the new pup and just get used to him being there.

as i said up there..it works for cats but i dont know about dogs..everyone that has taken a cat away from the rescue centre and has another cat at home, i say the same thing and not one person has ever come back to me to say it didnt work.
it wont work if one of the dogs/cats are at all familiar with the surroundings.. with cats i always say to the new owners.. if you are going to put them into a garage or shed or somewhere then dont leave a cat bowl or bed that belongs to one of the cats with them..it will then feel like the one cats property and he will be top cat then .

im not an expert and sorry to all if this sounds stupid as i said it works for cats a treat