Kramers turnover in class of thermodynamically open systems: Effect of interplay of nonlinearity and noises

► We uncover Kramers turnover for nonlinearly driven bath due to an external noise. ► Nonlinear driving exposes the system particles to a nonequilibrium environment. ► Not only internal noise, our system encounters other two multiplicative noises. ► Langevin equation contains the essential features of the interplay of these noises.