Nonlinearly partitioned Runge-Kutta (NPRK) methods are a new family of time integration schemes that generalize additive and component-partitioned Runge-Kutta. Specifically, NPRK methods allow one to treat factors within nonlinearities with differing levels of implicitness. For example, an IMEX-NPRK method can treat a factor of a nonlinear term implicitly while treating the rest explicitly. In this talk, I will give an overview of the NPRK framework and introduce multirate NPRK methods that treat each argument with a different timescale. I will also discuss order conditions and linear stability, and show several numerical experiments that demonstrate the performance of our new multirate methods.