Abstract T cells carrying receptors specific to an epitope are primed and differentiate in lymph nodes when they encounter their peptide-MHC counterpart displayed on dendritic cells. These epitopes are subunits of proteins derived from pathogens, but very few of the epitopes from any given pathogen elicit a measureable cell-mediated immune response. For infectious diseases lacking a protective vaccine, concurrent cellular immunity to several peptides may be necessary to target multiple stages of disease. In this work, we expand upon our previously developed computational model of T cell priming and differentiation in LNs to explore simultaneous induction of memory for multiple antigens. The model incorporates key parameters describing cell interactions, including pMHC-TCR binding parameters, cognate T cell frequency, and fraction of pMHCs specific to a TCR. Our results point to the importance of binding thresholds and pMHC fractions in determining immunodominance hierarchies. These findings are relevant to design of multi-subunit vaccines, where the aim is to simultaneously induce memory to several peptides.