The performance of coupled-cluster approaches with higher-than-doubly excited clusters, including the CCSD(T), CCSD (2)T, CR-CC (2,3), CCSD(TQ), and CR-CC(2,4) corrections to CCSD, the active-space CCSDt, CCSDtq, and CCSDTq methods, and the CC(t;3), CC(t,q;3), CC(t,q;3,4), and CC(q;4) corrections to CCSDt, CCSDtq, and CCSDTq resulting from the CC(P;Q) formalism, in reproducing the CCSDT and CCSDTQpotential energy curves and vibrational term values characterizing Be, in its electronic ground state is assessed. The correlation-consistent aug-cc-pVnZ and aug-cc-pCVnZ (n = T and Q) basis sets are employed. Among the CCSD-based corrections, the completely renormalized CR-CC(2,3) and CR-CC(2,4) approaches perform the best. The CC(t;3), CC(t,q;3), CC(t,q;3,4), and CC(q;4) methods, especially CC(t;3) and CC(q;4), outperform other employed approaches in reproducing the CCSDT and CCSDTQdata. Composite schemes combining the all-electron CCSDT calculations extrapolated to the complete basis set limit with the frozen-core CC(q;4) and CCSDTQ computations using the aug-cc-pVTZ basis to account for.connected quadruple excitations reproduce the latest experimental vibrational spectrum of Be-2 to within 4-5 cm(-1), when the vibrational spacings are examined, with typical errors being below 1-2 cm(-1). The resulting binding energies and equilibrium bond lengths agree with their experimentally derived counterparts to within similar to 10 cm(-1) and 0.01 angstrom.