Hoarding is a problem involving dogs, cats, and sometimes other species. Animal Hoarding is not about legitimate sheltering or rescue. It is a disorder. The Tufts University has a good working definition: Someone who accumulates a large number of animals; who fails to provide minimal nutrition, sanitation, and veterinary care; fails to act on deteriorating condition of the animals (including disease, starvation, and even death) or the environment (severely overcrowded and unsanitary conditions); and who fails to act on or recognize the negative impact of the collection on their own health and well being.
That said, there are no national guidelines for how many dogs to keep in your home. Some states including Illinois, New Mexico, and Vermont have enacted laws about hoarding, and some cities have ordinances regarding how many pets you can have in your home. Some of them pertain to dogs and cats, others may pertain to dogs only. You should check with your city to see what ordinances there might be in your community. One important tool that may be under-utilized are the housing, plumbing, sanitary, health, safety, and public nuisance codes that exist in every community.
If you suspect someone you know is hoarding animals, please contact your local animal care or welfare organization.
Tufts University Articles:
Working definition of a Hoarder: