Thermochemistry determined from careful analysis of the energy dependence of cross sections for collision-induced dissociation (CID) reactions has primarily come from the primary dissociation channel. Higher order dissociations generally have thresholds measured to be higher than the thermodynamic limit because of the unknown internal and kinetic energy distributions of the primary products. A model that utilizes statistical theories for energy-dependent unimolecular decomposition to estimate these energy distributions is proposed in this paper. This permits a straightforward modeling of the cross sections for both primary and secondary dissociation channels. The model developed here is used to analyze data for K+(NH3)x, x=2-5, complexes, chosen because the thermochemistry previously determined by threshold CID studies agrees well with values from theory and equilibrium high pressure mass spectrometry. The model is found to reproduce the cross sections with high fidelity and the threshold values for secondary processes are found to be in excellent agreement with literature values. Furthermore, relative thresholds for higher order dissociation processes appear to provide accurate thermodynamic information as well.