As an extension of two-level quantum bits (qubits), multilevel systems, so-called qu dits, where d represents the Hilbert space dimension, have been predicted to reduce the number of iterations in quantum-computation algorithms. This has been tested in the well-known [TbPc2]0 single-molecule magnet (SMM), which allowed implementation of the Grover algorithm in a single molecular unit. In the quest for molecular systems possessing an increased number of accessible nuclear spin states, we explore herein a dimeric Tb2-SMM via single-crystal μ-SQUID measurements at sub-Kelvin temperatures. We observe ferromagnetic interactions between the TbIII ions and cooperative quantum tunneling of the electronic spins with spin ground state | J z = ±6⟩. Strong hyperfine coupling with the TbIII nuclear spins leads to a multitude of spin-reversal paths, leading to seven strong hyperfine-driven tunneling steps in the hysteresis loops. Our results show the possibility of reading out the TbIII nuclear spin states via cooperative tunneling of the electronic spins, making the dimeric Tb2-SMM an excellent nuclear spin qu dit candidate with d = 16.