Optimizing Cellular and Humoral Immunity by Vaccinating With PCV13 Before and After CAR-T Therapy

Inclusion Criteria: * In good health as evidenced by medical history or diagnosed with relapsed or chemotherapy-refractory diffuse large B cell lymphoma (DLBCL), primary mediastinal B cell lymphoma (PMLBCL), transformed follicular lymphoma (TFL) high-grade B cell lymphoma (HGBCL) or Follicular Lymphoma. Patients must be under consideration for treatment with any CD19-targeted CAR T cell therapy, per institutional standards. Patients undergoing active vital organ testing with a planned apheresis date for CAR T cell therapy may be considered eligible. * Signed informed consent form in accordance with institutional and federal law policies * Stated willingness to comply with all study procedures and availability for the duration of the study * Male or female, age over 18 * For females of reproductive potential: use of highly effective contraception for at least 1 month prior to screening and agreement to use such a method during study participation Exclusion Criteria: * Pregnant or lactating woman, as evaluated by serum testing within 2 weeks of administration of the first vaccine. Only women of childbearing potential will undergo serum/urine pregnancy testing. A woman will be considered of childbearing potential unless she is status-post hysterectomy or tubal ligation or without menstrual periods in the preceding 12 months. * Common variable immunodeficiency or other inherited systemic immunodeficiency syndrome * History of severe allergy (e.g., anaphylaxis) to any component of pneumococcal conjugate vaccine 7 valent (PCV7), PCV13, or any diphtheria-toxoid containing vaccine. * Inclusion on a separate trial in which patients may be randomized or otherwise started on maintenance chemotherapies within the first 3 months of CD19-targeted CAR T cell therapy * Patients with significant psychiatric illness likely to affect compliance, as determined by the treating physician * Active or uncontrolled infections * Platelet count \<10,000 cells/microliter * Lymphocyte count \<200 cells/microliter * Intervenous immunoglobulin (IVIG) administration within one month of planned apheresis for collection for CD19-targeted CAR T cell manufacture * History of PCV13 administration within one month of planned apheresis for collection for CD19-targeted CAR T cell manufacture