Thermogravimetric analysis (TGA) is well-established for rapid reactivity assessment for reactions described by temperature and mass data alone. Many methods have been presented to quantify reactivity rates from TGA data, and some have been extended in the literature, creating a range of contrasting data for similar decompositions. A formalization of the Coats-Redfern method extended to encompass non-competitive, parallel reactions is presented. The method is tested with a range of theoretical decompositions containing numerous reactions with varying overlap and illustrates how reporting of TGA data could be improved. To increase robustness and confidence of predictions, an increase in the amount of data reported is suggested along with a novel method of comparing reactivities between experiments. The method is shown to compare decompositions using only the small amounts of data available when reactions overlap with tolerable accuracy for screening and indicative applications. The method is then applied to two biomass samples (willow and shea meal) decomposing in air and oxygen-enriched combustion environments, permitting critical evaluation of the estimations of the model. The method is able to accurately represent the willow decomposition, but the convoluted nature of the shea meal decomposition reduces the ability of the method to model this reaction. However, a comparison of the reactivities produced by the method to changes in the temperature at a maximum rate of decomposition indicates that for both biomasses the trends of oxygen enrichment of combustion atmospheres enhance combustion reactivity.