The ever-increasing demand for high data storage capacity has spurred research on development of innovative technologies and new storage materials. Conventional GByte optical discs (DVDs and Bluray) can be transformed into ultrahigh capacity storage media by encoding multi-level and multiplexed information within the three dimensional volume of a recording medium. However, in most cases the recording medium had to be photosensitive requiring doping with photochromic molecules or nanoparticles in a multilayer stack or in the bulk material. Here, we show high-density data storage in commonly available plastics without any special material preparation. A pulsed laser was used to record data in micron-sized modified regions. Upon excitation by the read laser, each modified region emits fluorescence whose intensity represents 32 grey levels corresponding to 5 bits. We demonstrate up to 20 layers of embedded data. Adjusting the read laser power and detector sensitivity storage capacities up to 0.2 TBytes can be achieved in a standard 120 mm disc.