We report on the multidimensional characterization of femtosecond pulse nonlinear dynamics in a tellurite glass graded-index multimode fiber. We observed novel multimode dynamics of a quasi-periodic pulse breathing which manifests as a recurrent spectral and temporal compression and elongation enabled by an input power change. This effect can be assigned to the power dependent modification of the distribution of excited modes, which in turn modifies the efficiency of involved nonlinear effects. Our results provide indirect evidence of periodic nonlinear mode coupling occurring in graded-index multimode fibers thanks to the modal four-wave-mixing phase-matched via Kerr-induced dynamic index grating.