  The nonlinear propagation of ion-acoustic (IA) waves (IAWs) in a four
component plasma medium (FCPM) containing inertial warm positive ions, and
inertialess iso-thermal cold electrons as well as non-extensive
($q$-distributed) hot electrons and positrons is theoretically investigated. A
nonlinear Schr\"{o}dinger equation (NLSE) is derived by using the reductive
perturbation method, and it is observed that the FCPM under consideration
supports both modulationally stable and unstable parametric regimes which are
determined by the sign of the dispersive and nonlinear coefficients of NLSE.
The numerical analysis has shown that the maximum value of the growth rate
decreases with the increase in $q$ ($q>1$), and the modulationally unstable
parametric regime allows to generate highly energetic IA rogue waves (IARWs),
and the amplitude and width of the IARWs increase with an increase in the value
of hot electron number density while decrease with an increase in the value of
cold electron number density. The applications of our investigation in
understanding the basic features of nonlinear electrostatic perturbations in
many space plasma environments and laboratory devices are briefly discussed.
