A system-reservoir nonlinear coupling model has been proposed for a situation where the reservoir is nonlinearly driven by an external Gaussian stationary noise which exposes the system particles to a non-equilibrium environment. Apart from the internal thermal noise, the thermodynamically open system encounters two other noises that are multiplicative in nature. Langevin equation derived from the resulting composite system contains the essential features of the interplay between these noise processes. Based on the numerical simulation of the full model potential, we show that one can recover the turnover features of the Kramers dynamics even when the reservoir is modulated nonlinearly by an external noise. (C) 2012 Elsevier B.V. All rights reserved.