If you're looking for a tower case, even a pretty large one, you're usually capped at about 15 drives, without getting really creative. You can get a case that has 9 top-to-bottom 5.25 bays, and fit it with 3 5x3 cages for a total of 15 hot-swap bays. I have seen a couple of tower cases that can fit 4 5x3 cages (like this one).
Otherwise, it's easy to find rack-mount cases on ebay for pretty cheap, with tons of hot-swappable bays, though I can't speak to their cooling abilities, especially if noise is a concern. You might also look into external eSATA enclosures, and connect one to your current box, if you don't mind the additional footprint.