Irradiated Donor Cells Following Stem Cell Transplant in Controlling Cancer in Patients With Hematologic Malignancies

Inclusion Criteria: * Patient with disease (stage) eligible per cohort * COHORT 1: patients undergoing high dose chemotherapy with autologous stem cell rescue and ?high-risk? disease as defined below: * Diffuse large cell lymphoma or peripheral T cell lymphoma (including specified World Health Organization \[WHO\] subtypes) not in computed tomography (CT)-positron emission tomography (PET) complete remission at time of high dose therapy * Diffuse large cell lymphoma with ?double hit? or ?double expressor? features * Diffuse large cell lymphoma or peripheral T cell lymphoma (including WHO specified subtypes) refractory to standard induction therapy OR relapsing within 1 year of treatment OR in greater that second complete remission (CR) * Mantle cell lymphoma not in CR1 * Multiple myeloma with ONE (or more) of the following high risk features: * Less than very good partial remission at time of high dose therapy * High Revised-International Staging System (R-ISS) (stage III ? 2 microglobulin \>= 5.5 plus lactate dehydrogenase \[LDH\] \> upper limit of normal \[ULN\] and/or del17p, t(4;14), t(14;16)) at time of diagnosis * Cytogenetics or fluorescent in situ hybridization (FISH) del17p * COHORT 2: patients with high risk disease having undergone an allogeneic hematopoietic stem cell transplant from a 10/10 human leukocyte antigen (HLA) matched donor with one of the following disease subtypes: * Acute myeloid leukemia (AML) in CR1 with high risk featur…