A new multidimensional spectroscopy (MUPPETS) was recently introduced (van Veldhoven, E.; et al. ChemPhysChem 2007, 8, 1761) that distinguishes between nonexponential relaxations that are due to heterogeneous dynamics and those that are due to homogeneous dynamics. This paper develops methods for the quantitative analysis of MUPPETS data and demonstrates the ability of this experiment to decompose a complex decay into its components. These methods have been applied to MUPPETS data on the ground-state recovery of auramine in methanol and on a mixture of auramine and coumarin 102 in methanol. The auramine is found to have two kinetically different components, even though the decay times are too similar to be distinguished in a one-dimensional experiment. The dynamics of each component are derived from the MUPPETS data in a model-free procedure in particular without assuming that the individual decays are exponential or that they have similar shapes. In fact, the component decays are each found to be nonexponential and to have different decay shapes. We suggest that the two components are due to ion-paired and nonpaired molecules. The effect of rotation on MUPPETS with all parallel polarizations is analyzed. The nonexponentiality in ground-state recovery signals due to the combination of rotation and population decay is shown to behave as a nearly ideal homogeneous nonexponentiality. This prediction is confirmed in a mixture of auramine and coumarin. MUPPETS allows the decay from the fast relaxing auramine to be removed from the mixture, leaving only the rotation/population decay of the coumarin.