Hooking up many different external HDs simultaneously

You can plug in that many drives via USB . . . but I wouldn't recommend it. The single biggest issue you're going to run into is the use of USB 2.0 (480Mb/sec shared across all devices on the controller). Unless you're using USB 3.0, you are going to seriously limit your disk throughput.

USB was intended for temporary (hot plug) or situations where very high data rate wasn't the primary concern. It's fine for a desktop backup drive, for example. If you need that many external disks and want decent performance at a low price point (assumptions made based on your question), you should look into eSATA (3Gb/sec). It won't cost you that much more, and the performance will be significantly better.

If this is intended as a permanent setup, there are eSATA disk enclosures available that will hold and power your drives. If it's a temporary setup, you can get SATA Port Multipliers (kinda like a SATA version of a USB Hub) to connect additional drives.

Mounting them is not the problem: It's going to be as slow as hell.

USB performance for external harddrives sucks at the best of times anyway.

Everything on the same USB controller/hub shares the bandwidth. You will have to spread them out over as many separate USB controllers as possible. Most motherboards only have 1 or 2 controllers so you will have to add additional USB controller cards.

Unless you have USB3 drives, controllers and/or hubs (Expensive!) performance will be awfull.

You are much better of plugin in several Pci-E SATA controllers and connecting the drives by SATA. Is a lot faster and probably cheaper as well.