In this paper, we present a coupled electron-pair (CEPA) type variant of the state-specific multireference coupled cluster (SS-MRCC) method [Mahapatra, U. S., et al. J. Chem. Phys. 1999, 110, 6171]. The method termed as SS-MRCEPA based on complete active space (CAS) can handle quasi-degeneracy of varying degrees over a wide range of potential energy curves (PECs), including regions of real or avoided curve-crossing. The method is size-extensive and avoids the intruder problem in a natural manner. Exploiting a two-dimensional CAS-based SS-MRCEPA method, we consider, in this paper, several demanding molecular systems that benefit from multireference description. The reliability of computational results of the method for PECs of the ground state of P4, H4, H-8, perpendicular insertion of Be into H-2, Li-2, and ground-state energy at the equilibrium point of CH2 will be discussed with respect to the parent SS-MRCC and full CI/large scale CI results. We have also reported the excitation energies corresponding to the ground states of H-8 and CH2 systems. The method has also been applied to study the bond breaking in the F-2 molecule which is a challenging task for any ab initio method. In all cases, the comparison is also made with the results obtained from other CC- and CEPA-type methods wherever available.