I've got four dogs, and it works out fine. I also have several other pets. Mind you, I also live in the country with a large backyard and house. The dogs go for a walk all the time and they all go into their crates when we have to leave the house. We simple say, "bedtime!" and they all cuddle up in their crates till we get home. We only have one large dog, the rest are small and therefore easier to manage. Its easy to fit them in the house, take them in the care, and walk them. We have no financial problems so we can afford to take care of all these pets.
How many dogs is too many? That depends on you. Some people think two are a handful. It also depends on the dog. Do you have three rambunctious dogs that make a mess and aren't very well trained? Or, do you have three large but well behaved dogs who aren't much of a hassle to take care of.