A general coupled cluster method that allows arbitrary excitations from a single reference-determinant is proposed and tested. The method is based on a generalization of the formalism of spin-strings and provides a unified method for the storage and manipulation of coupled cluster operators. An initial implementation of the method is discussed and used to study the convergence of the coupled cluster hierarchy for H2O and CH2 at equilibrium geometry, employing up to eightfold excitations. The energy and wave function contributions of the various excitation levels are examined. The dissociation curve of HF is also studied. Using single and double excitations from a minimal active space, the coupled cluster dissociation curve for HF shows a largest deviation from full configuration interaction curve of 1.3 mE(h), which decreases by an order of magnitude up on the addition of triple excitations out of the active space.