  We consider a coherently coupled nonlinear Schr\"odinger equation with
modulated self-phase modulation, cross-phase modulation, and four-wave mixing
nonlinearities and varying refractive index in anisotropic graded index
nonlinear medium. By identifying an appropriate similarity transformation, we
obtain a general localized wave solution and investigate their dynamics with a
proper set of modulated nonlinearities. In particular, our study reveals
different manifestations of localized waves such as stable solitons, Akhmediev
breathers, Ma breathers, and rogue waves of bright, bright-dark, and dark-dark
type and explores their manipulation mechanism with suitably engineered
nonlinearity parameters. We have provided a categorical analysis with adequate
graphical demonstrations.
