A lot depends upon who made your computer. For example, my wife's Dell has no provisions for an extra hard drive, no additional drive space in the cage, no additional plug on the cable...nothing. I ran into the same problem. I did not try to modify her drive cage...too much metal work to do. Instead, why not buy a hard drive enclosure that runs via your USB plug. Just mount your extra hard drive in it, and plug it in. Should work...
But please post your computer's manufacturer and model #...it may be that there is room there but maybe you have to remove the first hard drive casing...usually is done by removing a screw near the back and lifting the casing out. Look closly and see if there is a screw holding the casing in place....good luck...