The idea of combining the state-universal multi-reference coupled-cluster singles and doubles method (SUCCSD) with the multi-reference many-body perturbation theory (MRMBPT) is tested by approximating the cluster amplitudes of the SUCCSD formalism that carry only core and virtual orbital indices by their first-order MRMBPT estimates. The resulting SUCCSD(1) approach offers considerable savings in the computer effort, while providing the results that are as good as those obtained with the original SUCCSD method. Test calculations are performed for the lowest two totally symmetric singlet states of the H4 model system and methylene.