Don't think many current cases aside from server (rack mount) gear will do this anymore. I still have a old Lian Li full tower (PC-V2100b Plus II) that supported 12x3.5" drives without any mods at all (it also had 7x5.25 which you could easily add some hot-swap bays for even more 3.5" drives), and there was plenty of space to mod to add more.
You can find some older Supermicro SC846 chassis on ebay and other sites. They are 4U chassis that support 24 hot swap 3.5" drives (up to SAS3 depending on the exact 846 you get as there are different backplane models that supported different functions, from direct passthrough (needing up to 24 individual cables), SAS2, and SAS3). You can do a very easy mod to it replacing the fanwall with 120mm fans (there are 3d print models out there or you can simply zip tie the the fans together, instead of using the stock fans), but if you do that, make sure you are either actively cooling your CPUs and/or ensure the fans will still move enough CFM to be comparable to the original stock fans (I personally changed from passive CPU heatsinks to active ones so I could go with quieter fans).
There are newer supermicro cases that support 36 drives, but these don't support full height expansion (PCIe) cards, and you can't easily swap out the internal fans for 3x120mm ones as there isn't the same height in the case as they moved the motherboard tray/bottom upwards to make room for the additional 12 hot swap drives in the rear of the case under the motherboard, so it is a MUCH louder case as you need to essentially use the stock fans.