  We report an open three-state perturbed system with quasi-statically varying
Hamiltonian depending on the topological parameters. The effective system hosts
two second order exceptional points (EP2s). Here a third order exceptional
point (EP3) is explored with simultaneous encirclement of two EP2s by adiabatic
variation of topological parameters. We study the robust successive
state-exchange around the EP3. Applying adiabatic theorem, we estimate the
evolution of total phase accumulated by each state during encirclement; where
interestingly, the state-common to the pairs of coupled state picks up three
times phase shift of 2{\pi}. Such an exclusively reported scheme can be
exploited in potential applications of exceptional points, manipulating fewer
topological parameters in various non-Hermitian systems.
