In dealing with dogs, I kind of think a lot of it depends on the dogs themselves. Having 3 'easy' dogs shouldn't be as hard as owning 1 'difficult' dog that requires a lot of attention.
For example, I can no longer work, due to a disability...so I now can spend all day at home. This has allowed me to take on 2 dogs that I would have never considered if I had to be gone most of the day when I was working.
One dog, Jaya is almost feral, she was abused (hit with boards and whipped with tie down chains) for the first 5 years of her life and isolated in a back yard. I think she has improved a lot, due to my constant presence...if I wasn't able to spend the time with her, I know her progress wouldn't be any where near what it is now.
My other dog, HaHa, wasn't abused....but he is slightly retarded. I'm not sure for his first year, how much time the breeder spent with him, but at age 2, he was given to the shelter, almost starved to death because the breeder couldn't get him to eat, nor could the dog be sold because of his mental short comings and his physical appearance. His head is rather smallish and slightly misshaped, but also his issues with eating...made is so the breeder ended up letting the shelter have a go at finding him a home.
I know the shelter had him for a year, and so for a year HaHa (then known as Ruger) had people with him daily, and he's a Very sociable dog. The shelter never figured out how to put a lot of weight on him either...and was getting close to giving up on him. I decided to take him on because he was so friendly with people, I thought he could help in Jaya's social issues. And I thought I could try out things with this eating that the shelter didn't have time for. Like feeding him many times a day but just tiny amounts. That ended up working and now he's hat a healthy weight.
HaHa really, on an emotional level needs a person around, he's almost like a little 4 year old kind emotionally...if one could compare a full grown adult dog as behaving like an adult person. HaHa...would, as I said, be more like a small child due to his mental issues...he just never really grew up mentally.
However, he doesn't have separation anxiety, but I think having Jaya around helps with that a lot. He does follow me from room to room and can't seem to stand the idea of not being within a few feet of me while I'm home, though.
I think it would not have been good for him to be left alone for a long time if someone had adopted him then had to leave him alone and go to work all day. With his mental issues, it's kind of like abandoning a small puppy for a long time.
So...those two dogs...for me...are something that takes up a lot more of my time that what I would have been able to do if working. Again, I would not have taken in these 2 if not for the time factor.
I've almost always owned 2, and for a time 3 dogs...while I worked. But they were all easy keepers, no social issues -- people friendly. They didn't destroy my home while I was gone (and I had a fenced in yard and a doggy door). They also never barked all day while I was gone...my neighbors told me that...when I asked.
So, getting 3 dogs might not be a problem, if you take your time and chose a dog that fits in well with the other two you have and you know you can afford to feed and vet a 3rd pet. I did a huge amount of pre-adoption investigation before I got my last two 'problem' dogs. I knew what I was pretty much getting into...because I talked and emailed the rescue org and the shelter for as much information and for opinions about the dogs. I took on the dogs I did just because I was going to be home all day, and rather bored, and I have been around dogs my whole life and felt confident I could figure out how to help them....even if at the same time I knew I was going to have to play it by ear, especially with Jaya and go look for help in helping them.... which landed me here by the way : )
Weed out any dog even if you 'fell for it'...if it's truly not sounding like a good fit with your other dogs, for your life style and be honest with yourself if you won't have the time in working with it as much as it needs. I think that will make it a lot easier to have 3 dogs.