A new scheme for solving the coupled cluster (CC) amplitude equations for ground and excited electronic states in the state-selective multireference (MR) CC method based on the complete active space (CAS) reference wave function (CASCC) is proposed. The CASCC wave function is generated using a single formal reference determinant, which is one of the CAS determinants, as the origin of the configuration expansion. Some single and double excitations from other CAS determinants may be triple, quadruple, and higher excitations from the reference determinant. We show that one may include the contribution from these higher excitations indirectly by modifying the coupled cluster amplitude equations corresponding to the single and double excitations. The modification involves including projections against the higher excitations in the equations for the singles and doubles. Test calculations for the ground and the first excited state of the H-8-model system and for the singlet-triplet splitting of the CH2-biradical shows that the results improve with the use of the new scheme and become to the FCI benchmarks.