Where to rent with 13 dogs?

[N L Harrison]

This is a summarized version of events, but stray I rescued off the street gave birth to 7 puppies, bringing my total to 13. The shelters and foster networks are incredibly overrun, and I want to be responsible and not hand them off to random or possibly cruel strangers. Will I have to leave the state? I know there’s a limit of 4 unless you get a kennel license, so I’m also searching to find a place in which I can apply to obtain one. I’ve had great experience with private landlords in the past, and have found fellow pet lovers that didn’t charge pet rent, or accepted my larger dog (when he was alive) to live in an apartment without hassle. Just hoping there’s some way I can remain in California/SoCal (doesn’t have to be LA) and keep these babies. 

Thank you in advance.