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Time-resolved experiments with more than one period of incoherent time evolution are becoming increasingly accessible. When applied to a two-level system, these experiments separate homogeneous and heterogeneous contributions to kinetic dispersion, i.e., to nonexponential relaxation. Here, the theory of two-dimensional (2D) multiple population-period transient spectroscopy (MUPPETS) is extended to multilevel, excitonic systems. A nonorthogonal basis set is introduced to simplify pathway calculations in multilevel systems. Because the exciton and biexciton signals have different signs, 2D MUPPETS cleanly separates the exciton and biexciton decays. In addition to separating homogeneous and heterogeneous dispersion of the exciton, correlations between the exciton and biexciton decays are measurable. Such correlations indicate shared features in the two relaxation mechanisms. Examples are calculated as both 2D time decays and as 2D rate spectra. The effect of solvent heating (i.e., thermal gratings) is also calculated in multidimensional experiments on multilevel systems. [ABSTRACT FROM AUTHOR]