If you're desperate, you can screw a hard drive onto the back of the supermicro chassis. The square grill holes work well for screwing the hard drive in. I don't recommend doing this for general use, but if you're desperate and it's your own server (and not a customer's), then it can work.
You might have room inside the server to velcro a 2.5" HD or SSD in there, assuming you have an extra port on the RAID controller for it.
That can work as well. SSD's don't have exposed electronics, aren't very sensitive to heat or vibration, so you can pretty much throw them wherever you can fit them. In the 4 bay supermicro chassis, there is easily room above the 3.5" bay to fit in a 2.5" SSD if you don't mind it just floating around in there. I don't recommend this for hard drives since they are sensitive to vibration and need proper cooling, so should be mounted properly.