Multiphase continuum models are commonly used to predict the shock, combustion and detonation behavior of granular energetic mixtures containing solid reactants and gaseous products. These models often include phase interaction terms that formally satisfy the strong form of the Second Law of Thermodynamics and provide flexibility in distributing dissipation between phases arising from non-equilibrium phenomena. This work presents a thermodynamically compatible constitutive theory for reactive systems containing an arbitrary number of solid components. The theory represents a rigorous extension of the two-phase theory formulated by Bdzil et al., based on the well-studied Baer-Nunziato model. Forms of the gas-solid and solid-solid interphase sources suggested by general reactions of type A -> B are considered, where the combustion processes discussed in Bdzil et al. are treated as a special case. The model energetics are augmented by supplemental evolutionary equations that track local changes in phase temperatures due to dissipative and transport processes allowing for the identification of dominant energetic processes. This capability provides a mean to identify system parameters (e.g., metal particle size and mass fraction in metalized energetic mixtures) which optimize performance metrics. Detonation predictions are given for mixtures of granular HMX and aluminum to demonstrate model features and to highlight the effect of aluminum particle self-heating by oxidation on detonation. Predicted spatial profiles for mechanical fields, and the heating contributions from individual dissipative processes, illustrate how aluminum particle size can affect the coupling of oxidative heating to the explosive reaction zone. (C) 2015 Elsevier Ltd. All rights reserved.