Pets in San Jose?

I am transitions to a new job that will be located in downtown San Jose starting in July. I have two small dogs (16 pound corgi/jack russell mix and 14 pound schnauzer/poodle mix) and my partner has a dog as well (18 pound corgi). We have lived separately in the past but we are planning on living together with the move. How difficult will it be for us to find rentals that will accept 3 small dogs? We really want to have all 3 of the dogs and are willing to commute up to 45 minutes. Any advice or suggestions are much appreciated!