Currently in Los Angeles, residents are allowed up to three cats per household without a special kennel permit. Given the popularity of cats, the city may soon vote to allow residents to own up to five cats per household.
Then again, will any police officer really count the number of cats you own? Unless you start hoarding cats and stuffing them in your house or apartment so they overflow, chances are good you can safely keep as many cats as you wish as long as you properly care for them without the neighbors complaining.
As always, the more cats, the better. Provided, of course, that the more cats you have, the more time and money you can expend keeping all of them happy and healthy without letting them drive you crazy in the process.