Will you be ensuring there is no mess more than one pet would make?
Can you keep the animal mess down to a minimum? (fixing an area like a closet up where the litter boxes are kept so there's no dust or tracking, cleaning up all wastes immediately, steaming carpet and vacuuming out the AC and heater ducts regularly...)
Is the owner on the premises, or likely to visit? Do you have close-by neighbors who will complain or tell on you or are you in a duplex/condo situation where there is a common wall or ducting system that a neighbor with "allergies" or other issues might be able to make a fuss about more than one pet?
Can you make a case that two cats are less destructive than one, and easier to clean up after, asking permission for two. Do you have references and move out pictures from previous rentals showing how neat you left the premises after having multiple cats?
Now that I'm no longer renting, I can tell you none of the landlords or owners of the four houses we rented ever knew we had more than two cats and one dog, and we were always able to make the argument (using photographs and references) of the ability to clean after our pets and leave our previous lease better than we moved in. It also helps that I figured out how to patch wall to wall carpeting.
The last management company we rented from asked us where the cats were before we turned the keys back. We managed to convince them to let us have two (well, we had four) on the contract instead of the one after references and before/soon to be after pictures of the place we were moving out of, so long as we paid deposit for the two.
They went looking for where the litterboxes would be, and couldn't find any evidence of cats in the house.
What I did was set up a large tarp around the floor and sides area the corner of the room where the litter boxes were to go, and I have a felt-covered cardboard structure that goes along the sides and curves over as a "roof" to keep the dust down, then have towels and cat litter rugs out four feet over the tarp on the floor to keep the dust and grit from getting onto the floor. It was a pain and took up space, but I never had a dust problem or nasty smells.
In fact the kidlet did far more damage than the pets ever did. But I never had pet damage in any rental, even with a young dog and a pair of kittens.
But when you are leasing and know you'll have more than one pet you should always inquire. If it seems like they may be hard and fast about it, tell them you have plans to ensure the place will remain clean, will provide plans and pictures of mess remediation efforts, and you'd pay an extra pet deposit to cover additional animals. Try to get a year lease rather than month to month. They'll be more accommodating if they feel you're going to make an investment in staying there rather than just looking for a place to crash (or trash) until you can find something better.
But ultimately, it's best to be clear about the possibility of them finding out you might have more than one pet.
Final warning - if your pets are rambunctious, noisy, or damaging, just keep on looking to the next house that would take more than one, because the damage unruly pets cause is what will ultimately give them grounds to get you evicted.
Honestly, trailer parks are probably your best bet in the long run, if you can afford to purchase a fixer and the lot rental. That's what we did - lot rental is less than quarter of a house rental, there's little yard upkeep (planter-box gardening), the utilities are sub-metered, there's a nice clubhouse and amenities, and we were able to purchase our double-wide cash on a bank estate sale. Took us two weeks to make it habitable, had to get new/used appliances and we're still renovating (finishing the hardwood flooring in every room), but the four cats are happy and we still have plenty of room for $750 a month lot rental and $155 a year "residence tax" - over 1500 sq ft of house, two large storage sheds, and a car port. And our neighbor's trailers are 18 ft. away - farther apart than most houses.
The management in a trailer park usually doesn't care what you keep in your trailer home, so long as they stay indoor pets and don't create trouble to the other residents.
As for legal limits, it depends on the city in Orange County, CA you will be moving to.
Every city has different rules; some have two pets only period, unless you're keeping something like an aquarium, some allow two each dogs and cats, with any number of other indoor pets allowed so long as they don't create a nuisance, health or safety hazard, some counties have no more than 2 outdoors and 4 indoors (dogs and cats). Here in San Diego county, there's a small suburb/un-incorporated "community" that requires if you have any more than 2 of a species must get a special license no matter if they're indoor or outdoor (due to the politics of having feral colonies and rescues in a neighborhood).
Anyway, there should be a city or county website that has a residential animal compliance code for the area you are moving into.
Good Luck.
Haele
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