I think it depends on a lot more then just numbers.
It depends on the person (or people) who handle/own them, the dogs, their breeds (energy level, drive, nerves, how compatible they are with living with others.. etc, etc.), and it also depends on the energy of the house hold.... it all has to match up.
For instance. My grandmother was an Akita breeder back in the days, she trained and showed them. She had multiple dogs through most of her adult life. When the Akita's passed away and she stopped breeding (her age and health just didn't agree with that way of life) she had her little Chihuahua and a personal protection trained Doberman. She handled all of this with ease. Never an issue. The house was peaceful and the dogs were happy. She was able to handle working dogs and all their requirements. She understood the breeds she owned and that made for a happy household.
Growing up, we had 3 golden retrievers. Later, my grandmother moved in with us with her older chihuahua. Through those years, we also rescued 2 pit bulls, and an american bull dog. All lived in the same house. 2 intact females, 1 spayed female, 2 neutered males, 2 intact males. We had 1 small dog fight. Which ended quick without injury. All dogs lived without kennels or crates, the females were separated when their heat cycle came around. No puppies came from this, and no blood was ever shed. We were not a highly "dog educated" family, we just had my grandma's knowledge and common sense. We were just an average American family. How we did it, according to most opinions... I don't know. But it worked just fine.
My brother and his wife have 3 rescued pit bulls (one that was raised in our home with the goldens) and a doberman. They have a small farm and the dogs are all indoor dogs. No crates, no kennels, no dog runs..... never had any serious issues. 2 intact males, 1 intact female (sterile), and 1 spayed female.
I have 2 GSDs. One male (WGSL), one female (ASL)... both fixed. I plan on adding a third within the next few years (will be a GWL). I'm not worried. With my experience with dogs, I feel I do a good job at matching them all up nicely. And if needed... I am willing to crate and rotate. However, this is not the plan. I understand what my dogs require and IMO are some of the best behaved dogs here in my part of town.
I understand at this point, I am not considered the general public. And maybe my siblings are not either, since we grew up in a multiple dog home. However, my grandma started out on her own (she grew up with NO animals allowed and didn't start breeding until after her kids were grown and out of the house), and my parents learned as time went by.
The one thing that makes the biggest difference is picking the breed that fits your home, temperament, family, and lifestyle. Can all families handle 3+ GSDs (or any type of working dog)... absolutely not! Can all families handle 3+ large breed dogs... no. Can all families handle 3+ small dogs.... again, no. Can all families handle just 1 dog.... no! People too often go with what is "sooo cute!" instead of actually researching and understand the breed and it's nature. This is what leads to dogs being out of control most of the time. Not the number of which they own. Very rarely do I meet a person with multiple dogs out of control that understand their breed of choice and how to work with them... which is exactly what the problem is!
I do agree that once you hit 3, you switch to pack mentality. The problem comes when the owner just can't find the time and commitment to each dog.... With certain breeds (i.e. GSDs, Pit Bulls, Huskies, etc), this also requires a good amount of knowledge of the breed (and their individual dogs temperaments) and their pack mentality in order to keep the peace. Other breeds.. like... golden retrievers, require a bit less and make it much more possible for the average joe and jane to own a "pack".
Just my $0.02 in what I've seen and experienced over the years.