New cats will be unlockable depending on the total number of photos you have collected. It requires having collected 105 total photos to unlock all cats.
Every new cat requires that you have 5 more photos in your total to unlock. You do not actually "spend" the photos to unlock the cats so don't worry about impacting your photo collection progress.
The fastest way to collect photos is by playing Procedural on the Pawliday Den level (smallest level) or Box Purradise (most photos in one room) and completing goals that reward photos as well as grabbing the 4-6 in the level each try.