Depends on the characters involved, like it would with people, I guess?
I have a happy story for you, though.
We had a 2 year old staffy, much loved 'only dog'. For some reason, I decided to look into getting a mini bull terrier and when I rang round breeders, they all had 2 year waiting lists but one breeder said she had no pups but there was an adult female show dog she was thinking of selling on... would I be interested?
Staffy was great with other dogs on walks, etc, but I had no idea how he'd take to another adult dog the same age as him sharing his house... I felt it would be easier with a pup but what the hell, went to look at the 2 year old bullie anyway.
And it was love at first sight, me and her. She literally hurled herself into my arms the moment she saw me, and into my heart, too. I had to have her.
We had young kids so by chance still had baby gates up. That proved useful. Brought her home - she was a show dog so used to being around other dogs. But still no idea how she'd feel about sharing a home with another pooch.
Put him in the kitchen one side of baby gate with the door wide open so he didn't feel excluded (it was summer which helped). And the other side, she was in the living room. I read up on it and read to make the first thing you do with the dogs something on neutral territory they'll both love. So we walked them. They seemed to like eachother. But we kept them either side of the gate and would have done for as long as it took. By about Day 4 or 5 it was obvious they were mad about eachother. Both spent all day sat next to the gate, looking longingly at the other. Gate was opened... voila. Two bonded dogs.
That whole first week we walked them together - with at least 2 of us so each had a lead and a dog, separate but together. We fed them either side of the gate at the same time as eachother. All the nice things happened with them close to eachother.
Sadly he died only 4 years later, aged only 6 and she grieved appallingly. Even so I took the decision not to get another dog, and it took her months to adjust to being alone. But it was better for her than to risk getting another dog she hated or who hated her as she was quite a sensitive little soul. She died last year aged 14.
I think we managed every second they spent together that first week, and limited it. Always 2 of everything though - 2 dog chews (she'd eat faster than him and then steal his which sometimes he was unimpressed by). 2 bed - he had his crate he'd had since a pup and she slept on the sofa. She never went in the crate and it was always his space. That helped a lot, too that the original dog was crate-trained.