Thermaltake S370 WS; Mid Tower; Wood Front Trim; 4x120mm Fans Included; 410mm GPU Clearance;up to E-ATX; Hidden Connector Support (ATX/mATX); Vertical GPU Support; Black; CA-11J-OOM1WN-00

Something like a S370 holds four 3.5" cleanly, and a 9300-8i can talk to 8+ drives - together they'll set you back about $100. The drives will take up space either way. You can either have everything-in-one-place and reliable with internal HDDs... or you can deal with the unreliability and clutter of an external USB solution. I'd actually plan for the future... and get a case that holds 8 drives: so you don't deal with this problem again in a couple years. Lots of options: Good Luck!