As an adoptive cellular therapy, Chimeric Antigen Receptor T cell (CAR T cell) therapy has shown remarkable success in hematological malignancies but only limited efficacy against solid tumors. Compared with blood cancers, solid tumors present a series of challenges that ultimately combine to neutralize the function of CAR T cells. These challenges include, but are not limited to, antigen heterogeneity - variability in the expression of the antigen on tumor cells, as well as trafficking and infiltration into the solid tumor tissue. A critical question for solving the heterogeneity problem is whether CAR T therapy induces bystander effects, such as antigen spreading. Antigen spreading occurs when CAR T cells activate other endogenous antitumor CD8 T cells against antigens that were not originally targeted. In this work, we develop a mathematical model of CAR T cell therapy for solid tumors that considers both antigen heterogeneity and bystander effects. Our model is based on in vivo treatment data that includes a mixture of target antigen-positive and target antigen-negative tumor cells. We use our model to simulate large cohorts of virtual patients to better understand the relationship involving bystander killing. We also investigate several strategies for enhancing bystander effects, thus increasing CAR T cell therapy's overall efficacy for solid tumors.