  The physics of topological singularities, namely exceptional points (EPs),
has been a key to wide range of intriguing and unique physical effects in
non-Hermitian systems. In this context, the mutual interactions among four
coupled states around fourth-order EPs (EP4s) are yet to be explored. 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 exhibit
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 coupled 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 new successive state-switching phenomenon among them; which proves
to be robust even in the presence of different order of EPs. Implementing the
relation of the perturbation parameters with the coupling control parameters,
we exclusively report a region to host multiple EP4 in a specific system. The
chiral behaviour of successive state-exchange has also been established near
EP4. Proposed scheme enriched with physical aspects of EP4s should provide a
new light manipulation tool in any anisotropic multi-state integrated system.
