The physics of topological singularities, namely, exceptional points (EPs), has been a key to a wide range of intriguing and unique physical effects in non-Hermitian systems. In this context, exploration of the mutual interactions among the states in four-level systems around fourth-order EPs (EP4s) is lacking. Here we report a four-level parameter-dependent perturbed non-Hermitian Hamiltonian, mimicking quantum or wave-based systems, to explore the physical aspects of an EP4 analytically as well as numerically. The proposed Hamiltonian exhibits different orders of interaction schemes with the simultaneous presence of different higher-order EPs. Here an EP4 has been realized by mutual interaction between four states with proper parameter manipulation. We comprehensively investigate the dynamics of corresponding coupled eigenvalues with stroboscopic parametric variation in the vicinity of the embedded EP4 to establish a successive state-switching phenomenon among them, which proves to be robust even in the presence of different orders of EPs. Implementing the relation of the perturbation parameters with the coupling control parameters, we report a region to host multiple EP4s in a specific system. The chiral behavior of successive state exchange has also been established near the EP4. The proposed scheme, which is enriched with physical aspects of EP4s, should provide a unique light manipulation tool in any anisotropic multistate integrated system. © 2019 American Physical Society.