The complete orthogonally spin-adapted Hilbert-space (or state-universal) coupled-cluster (CC) theory involving singly and doubly excited clusters for a model space spanned by two closed-shell configurations is considered. Explicit expressions for the previously neglected cubic and quartic coupling terms are derived using diagrammatic methods of many-body perturbation theory and graphical methods of spin algebras. The resulting formalism has been implemented and the general purpose ab initio program has been written using newly developed procedure for improving the convergence of the reduced linear equation method. Results of the pilot calculations for the two lowest singlet states of the minimum basis set and double zeta plus polarization basis H4 models as well as for the CH2 molecule at equilibrium and displaced geometries are presented and compared with the available single-reference CC and configuration interaction data. They indicate negligible role of the cubic and quartic coupling terms, which justifies the validity of approximations considered so far.