In this talk we present a mixed precision and mixed model approach for multi-stage methods. We show that Runge-Kutta methods can be designed so that certain costly intermediate computations can be performed as a lower-cost computation without adversely impacting the accuracy of the overall solution. In particular, a properly designed Runge-Kutta method will damp out the errors committed in the initial stages. This is of particular interest when we consider implicit Runge-Kutta methods. In such cases, the implicit computation of the stage values can be considerably faster if the solution can be of lower precision, lower tolerance, or cheaper model. We provide a general theoretical additive framework for designing mixed precision Runge-Kutta methods, and use this framework to derive order conditions for such methods. Next, we show how using this approach allows us to leverage cheaper computation of the implicit solver while retaining higher accuracy in the overall method. Finally, we perform a stability analysis which informs how to design methods that will be stable for different types of splittings to determine the cheaper but less accurate model.