What you have, are basically 3x choices:
- Jerry-rig the additional drives somehow inside your PC case.
- Replace the PC case with the one that has more drive bays.
- Or get bigger drives to replace the existing ones rather than adding to them. Explanation below;
For example, if you currently have e.g 500GB SSD + 2x 1TB HDDs; buy 1TB SSD and 4TB HDD. With that, you'll gain double the space while freeing up one 3.5" drive slot, keeping only 1TB SSD and 4TB HDD in the system. Also, if you need to have several drives in the OS (e.g C: D: E: F: etc), just split the one big HDD into smaller partitions. E.g you can split the 4TB drive into 4x 1TB partitions. OS still sees your drives as separate drives while in reality, they all are one drive.