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 features (European Leukemia Network \[ELN\]) at presentation

    * Diagnostic sample with either t(6;9), t(9;22), 11q23, inv 3, -5, -7, del17p, complex cytogenetics, NPMwt-flt3ITD+, OR p53 mutation (mut); patients whose samples have mutations in RUNX1 or ASXL1 are also eligible (unless the patient has favorable cytogenetics)
  * AML in CR1 with measurable minimal residual disease (MRD) by molecular (e.g., myeloid mutation profile, polymerase chain reaction \[PCR\] for NPM1, core-binding factor \[CBF\], mixed lineage leukemia \[MLL\]) or flow cytometry
  * AML not in CR1 (including patients with morphologic CR but with incomplete recovery, CRi)
  * Myelodysplastic syndrome (MDS) with complex cytogenetics, 17p deletion or p53 mutation, or JAK2 or RAS mutation
  * Treatment-related MDS or AML
  * Acute lymphoblastic leukemia (ALL) not in CR1
  * ALL with MRD
  * Any hematologic malignancy relapsed or with persistent disease after allogeneic hematopoietic stem cell transplant
  * Multiple myeloma
  * Non-Hodgkin lymphoma (NHL) with chemoresistant disease at time of transplant
  * Any patient undergoing allogeneic hematopoietic stem cell transplant and an anticipated rate of relapse \> 80% based upon published data and for which there is consensus amongst the Hematologic Malignancies Tumor Study Group that enrollment is appropriate
* Availability of a genetic child, genetic parent or sibling as a potential HLA haploidentical donor
* Meets standard eligibility requirements for high dose chemotherapy with autologous stem cell rescue (COHORT 1) or allogeneic hematopoietic stem cell transplant (COHORT 2) and has signed consent for those procedures
* DONOR: Donor must be related to patient and be partially (\>= 3/6 antigen) HLA-matched
* DONOR: Donor must meet all Robert Wood Johnson (RWJ) Blood Services requirements for hematopoietic stem cell donation including:

  * Age \>= 18 years old;
  * Normal hemogram (white blood cells \[WBC\] 4.0-10.0 x 10\^3/mm\^3; platelet count 150,000 to 440,000/mm\^3 ; hemoglobin/hematocrit; 12.5-18 g/dl, 38 to 54%
  * Not pregnant or lactating;
  * Not human immunodeficiency virus (HIV)-1, HIV-2, hepatitis C virus (HCV), hepatitis B core or human T-cell lymphotropic virus (HTLV)-I/II seropositive; hepatitis B surface antigen (HB S ag) (-); meet other infectious disease screening criteria utilized by RWJ Blood Services;
  * No uncontrolled infections, other medical or psychological/social conditions, or medications that might increase the likelihood of patient or donor adverse effects or poor outcomes;
  * Meet other blood bank criteria for blood product donation (as determined by RWJ Blood Center screening history and laboratory studies)

Exclusion Criteria:

* Non-English speaking person
* Patients undergoing haploidentical allogeneic hematopoietic stem cell transplants are not eligible; patients undergoing \< 10/10 HLA allele matched allogeneic transplant are not eligible
* Pregnant women
* DONOR: Non-English speaking person
* DONOR: Pregnant women