If you’re not worried about keeping the disks on the original cases then I am a big fan of disk folders (such as the following) and putting the cases away elsewhere.

Case Logic CD/DVDW-92 100 Capacity Classic CD/DVD Wallet (Black) https://www.amazon.com/dp/B00005ATMD/ref=cm_sw_r_cp_api_fab_cUMFFbPMH11AB