Previous experimental studies suggest that Mycobacterium tuberculosis inhibits a number of macrophage intracellular processes associated with antigen presentation, including antigen processing, MHC class II expression, trafficking of MHC class II molecules, and peptide-MHC class II binding. In this study, we investigate why multiple mechanisms have been observed. Specifically, we consider what purpose multiple mechanisms may serve, whether experimental protocols favor the detection of some mechanisms over others, and whether alternative mechanisms exist. By using a mathematical model of antigen presentation in macrophages that tracks levels of various molecules, including peptide-MHC class II complexes on the cell surface, we show that mechanisms targeting MHC class II expression are effective at inhibiting antigen presentation, but only after a delay of at least 10 h. By comparison, the effectiveness of mechanisms targeting other cellular processes is immediate, but may be attenuated under certain conditions. Therefore, targeting multiple cellular processes may represent an optimal strategy for M. tuberculosis (and other pathogens with relatively long doubling times) to maintain continuous inhibition of antigen presentation. In addition, based on a sensitivity analysis of the model, we identify other cellular processes that may be targeted by such pathogens to accomplish the same effect, representing potentially novel mechanisms.