Before revision:  In addition to defining these methods, we prove that they may be viewed as specific instances of generalized-structure additive Runge--Kutta (GARK) methods, and derive a set of order conditions on the IMEX-MRI coefficients to guarantee both third and fourth order accuracy for the overall multirate method.
After revision:  In addition to defining these methods, we prove that they may be viewed as specific instances of generalized-structure additive Runge--Kutta (GARK) methods, and derive a set of order conditions on the IMEX-MRI-GARK coefficients to guarantee both third and fourth order accuracy for the overall multirate method.