I don't mean to be rude, but this is probably going to sound like it.
You have your priorities backward. Basically, the way you're planning the build, it's a mountain of wastage, not a mountain of storage.
A mid-tower case has 4 to 5 3.5" bays, and maybe 1 or two floppy drive bays (known as 'exposed' bays). It also has three or four usable 5.25" bays. The floppy bays take a regular hard disk no problem, except it's held with two screws instead of four. I have disks installed like this and it's not an issue. Each 5.25" bay can house one drive using a single adapter, and using a CM bay adapter or similar, you can mount 4 drives in 3 bay space.
This is how a normal Elite can hold 9 drives, as mine can. An no modding required at all, just a few pieces of metal (I'm selling a few of these adapters - though I'm not shipping anywhere, you're welcome to have a look at my thread to see what they look like). Now, if you want more drives and/or more room, a CM690 will do 10 drives and so will a N300, if you convert the bays correctly. That is precisely one more drive than the Elite can. Maybe the HAF X and so on will do one or two more.
Unfortunately, even in a very large case cable clutter is inevitable when you install more than 3 SATA cables. This is unavoidable because inherently wiring up a drive is messy. If this is a problem I would advise you to buy 10 external cases and install a drive in each one, and connect them using USB hubs. You're not going to have it all.
I have a monster of a case, the Xigmatek Elysium, and I have 5 devices (2 optical, 1SSD and 2 hard disk drives) plus the cables for the front panel eSATA and the drive dock - so 7 cables total, and you won't believe how messy it is in spite of all the cables going through the back of the tray. At some time closing the side panel is a challenge too. The case itself will handle 14 drives using adapters, and I'm not sure of many cases that will do more. It does come with two 4-in-3 modules which actually work as 3-in-3 modules because of the shitty East Asian design 'gurus' who managed to get a lot of things wrong when they did this case. I have had a rig with 5 drives and excellent cable management for the day (the Antec Solo, circa 2005), and it was still a pain in the ass because of the thick and inflexible SATA cables plus a power cable. No matter how great you are at cabling, 5 drives or more is gonna be spaghetti kitchen redux.
Only when you actually implement something like this you will realise how ambitious it is to make special purpose rigs. Compromises that you wouldn't make in other kinds of rigs are inevitable here. In my fileserver, all the cables are on the motherboard side. This makes it look very messy, but every cable has a coded tag and changing a drive is a matter of 15 seconds excluding power up and power down. I don't mind the clutter and having a very low power board means the reduced airflow does not cause any issues there either. Serviceability and identification are key concerns in that case and I manage fine.
Yes, you could get some of the fancy Lian Li cabling and bay multiplier options but for basically a fileserver I don't see the point. Still, it's your money and you're entitled to do with it as you see fit.
I hope you have enough information to make a decision now. I will leave you to it, with my best wishes.
