History of allogeneic organ transplant History of allogeneic organ transplant History of allogeneic organ transplant History of allogeneic organ transplant History of organ transplant Has a history of primary immunodeficiency or an allogeneic organ transplant History of primary immunodeficiency, history of allogeneic organ transplant that requires therapeutic immunosuppression History of organ transplant. History of allogeneic organ transplant Patients who have undergone a prior allogeneic hematopoietic or (other organ) transplant History of allogeneic organ transplant History of allogeneic organ transplant History of allogeneic organ transplant History of allogeneic organ transplant History of allogeneic organ transplant. History of organ transplant History of allogeneic organ transplant History of allogeneic organ transplant History of allogeneic organ transplant History of allogeneic organ transplant History of allogeneic organ transplant History of allogeneic organ transplant. History of allogeneic organ transplant History of allogeneic organ transplant History of organ transplant. History of allogeneic organ transplant History of allogeneic organ transplant History of allogeneic organ transplant History of allogeneic organ transplant or autoimmune disease History of allogeneic organ transplant History of allogeneic organ transplant History of allogeneic organ transplant History of allogeneic organ transplant History of allogeneic organ transplant History of allogeneic organ transplant History of organ transplant History of organ transplant. History of allogeneic organ transplant History of allogeneic organ transplant. History of allogeneic organ transplant History of allogeneic organ transplant History of allogeneic organ transplant Patients with history of organ transplant History of allogeneic organ transplant Patients with history of organ transplant History of organ transplant History of allogeneic organ transplant History of allogeneic organ transplant History of allogeneic organ transplant History of allogeneic organ transplant History of allogeneic organ transplant History of major organ transplant. History of organ transplant. History of allogeneic organ transplant History of allogeneic organ transplant History of allogeneic organ transplant History of allogeneic organ transplant History of allogeneic organ transplant History of organ transplant. History of major organ transplant History of allogeneic organ transplant History of organ transplant History of major organ transplant History of having received allogeneic organ transplant History of allogeneic organ transplant History of allogeneic organ transplant Has undergone 1 allo-HSCT from any donor (related or unrelated with any degree of HLA matching) and any donor source (bone marrow, peripheral blood stem cells, or cord blood) for a hematologic malignancy or disorder. Recipients of myeloablative and reduced-intensity conditioning regimens are eligible. Patient deemed to be suitable candidate for myeloablative or reduced intensity conditioning allogeneic HSCT using PBSC or marrow as stem cell source DONOR: Only filgrastim (G-CSF) mobilized PBSC only will be permitted as a hematopoietic stem cell (HSC) source on this protocol DONOR: Bone marrow will be the only allowed stem cell source Have undergone allogeneic stem cell transplantation (alloSCT) from any donor source (matched unrelated donor, sibling, haplo-identical) using bone marrow, peripheral blood stem cells, or cord blood. Recipients of non-myeloablative, myeloablative, and reduced intensity conditioning are eligible Patients must have a related or unrelated peripheral blood stem cell donor that meet one of the following criteria: Participant is considered a suitable candidate for HCT and has an acceptable source of allogeneic donor stem cells, as defined per institutional practice (allogeneic HCT for any donor source [matched sibling, unrelated donor (URD), mismatched URD, related haploidentical, or umbilical cord blood] and any graft source [umbilical cord, BM, peripheral blood (PB)], and any conditioning [myeloablative conditioning (MAC), reduced intensity conditioning (RIC), or non-myeloablative conditioning (NMA)] will be permitted). DONOR: must be capable of and consent or assent to donation of peripheral blood stem cells Patient must have an adequate supply of stem cells for transplant harvested prior to study enrollment, with adequate supply defined as 3 x 10^6 cluster of differentiation (CD)34+ cells/kg for peripheral blood stem cells (PBSC); cell mobilization method will be left up to the treating physician's discretion and may include mobilization growth factor alone or mobilization after chemotherapy; if patient is unable to mobilize the proper amount of peripheral stem cells, bone marrow may be harvested as the source of hematopoietic stem cells; in this instance, 3 x 10^8 mononuclear cells/kg will be considered adequate; if necessary, a combination of peripheral stem cells and bone marrow can be used Any donor type (e.g., related, unrelated) or stem cell source (bone marrow, peripheral blood, cord blood). PHASE I: Patients who underwent an allogeneic hematopoietic stem cell transplantation from any donor source for acute lymphocytic leukemia PHASE II: Patients who underwent an allogeneic hematopoietic stem cell transplantation from any donor source for acute lymphocytic leukemia Have identified a backup cells source in case of engraftment failure. The source can be autologous, related or unrelated. Have undergone Allogeneic Stem Cell Transplanttaion (alloSCT) from any donor source (matched unrelated donor, sibling, haplo-identical) using bone marrow, peripheral blood stem cells, or cord blood. Recipients of non- myeloablative, myeloablative, and reduced intensity conditioning are eligible A person (such as a haploidentical family member) or unit of cord blood must be identified as a source of back-up cells source in case of engraftment failure Any donor type (e.g., related, unrelated) or stem cell source (bone marrow, peripheral blood, cord blood); recipients of non-myeloablative and myeloablative transplants are eligible Hematopoietic stem cell source is either with peripheral blood, bone marrow or cord blood. No more than 1 antigen mismatch at HLA-A, -B, -C, -DRB1 or -DQB1 locus for unrelated donor with peripheral blood and bone marrow as the hematopoietic stem cell source; and DONOR: Donors >= 18 years of age must be the same individual whose cells were used as the source for the patient’s original stem cell transplant Marrow is the preferred source of stem cells from the HLA-haploidentical donor, however, peripheral blood mononuclear cells (PBMC) could be used as stem cell source, after clearance with the Fred Hutchinson Cancer Research Center (FHCRC) principal investigator, in the case of difficulties or contraindications to bone marrow harvest from the donor DONOR: Marrow is the preferred source of stem cells from the HLA-haploidentical donor, however PBMC could be used as stem cell source, after clearance with the FHCRC principal investigator, in the case of difficulties or contraindications to bone marrow harvest from the donor Stem cell source Bone marrow (preferred source) OR peripheral blood stem cells of filgrastim [G-CSF]-stimulated donors OR cord blood Have identified a backup cells source in case of engraftment failure; the source can be autologous, related or unrelated Donor stem cell source can be either peripheral blood or bone marrow Cord blood as a donor source is not acceptable Have undergone first allogeneic hematopoietic stem cell transplantation (allo-HSCT) from any donor source using bone marrow, peripheral blood stem cells, or cord blood for hematologic malignancies. Recipients of nonmyeloablative and myeloablative conditioning regimens are eligible. HLA Matched Related Donor: G-CSF mobilized peripheral blood mononuclear cell (PBMC) only will be permitted as a hematopoietic stem cell (HSC) source on this protocol Back-up stem cell source DONOR: Peripheral blood stem cells (PBSC) only will be permitted as a HSC source on this protocol Have undergone first allo-HSCT from any donor source (matched unrelated donor, sibling, haploidentical) using bone marrow, peripheral blood stem cells, or cord blood for hematologic malignancies. Recipients of nonmyeloablative and myeloablative transplants are eligible. DONOR: Meets standard institutional criteria for GCSF mobilized peripheral blood stem cell (PBSC) donation Use of cord blood as the source of hematopoietic cells is not allowed. DONOR: Only filgrastim (G-CSF) mobilized PBSC only will be permitted as a hematopoietic stem cell (HSC) source on this protocol DONOR: Marrow will be the only allowed hematopoietic stem cell source Unrelated cord blood will be used as a source of hematopoietic support if a 5 or 6/6 related or 6/6 unrelated bone marrow donor is not available, or if the tempo of a patient's disease dictates it is not in the patient's best interest to wait for an unrelated marrow donor to be procured Have identified a back-up cell source in case of engraftment failure; the source can be autologous, related, or unrelated UNRELATED DONORS: Only G-CSF mobilized PBMC will be permitted as a HSC source on this protocol DONOR: Only G-CSF mobilized peripheral blood mononuclear cells (PBMC) only will be permitted as a hematopoietic stem cell (HSC) source on this protocol DONOR: Bone marrow is the preferred cell source Patients after allogeneic stem cell transplantation from a related or unrelated, HLA-matched or mismatched donor with the diagnosis of transplant related microangiopathy. Patients having received any of the following stem cell sources are eligible: G-CSF mobilized peripheral blood stem cells, bone marrow, umbilical cord blood. For Pre-allo Part A (before stem cell transplant): Partially matched donors (related or unrelated) and umbilical cord blood cells are excluded as the source of hematopoietic stem cells Back-up stem cell source Have identified a back-up cells source in case of engraftment failure; the source can be autologous, related or unrelated Any diagnosis, donor or source of hematopoietic stem cells (HSC) is allowed, including donor leukocyte infusions (DLI) Stem cell source: bone marrow, peripheral blood stem cell DONOR: Must be willing and able to undergo peripheral blood stem cell (PBSC) collection Scheduled to undergo a hematopoietic stem cell transplant for any cancer or non-cancer illness from any autologous, related or unrelated donor source including bone marrow, peripheral blood progenitor cell, or umbilical cord blood The patient must be undergoing allogeneic HCT from any donor (including matched related) with any stem cell source for any underlying condition Patients designated to undergo myeloablative or intermediate intensity allogeneic peripheral blood or bone marrow hematopoietic cell transplantation; consent will be obtained prior to admission for HSCT; patients receiving any donor source of stem cells are eligible; eligible conditioning regimens are those defined as myeloablative by the American Society of Blood and Marrow Transplantation (ASBMT) consensus criteria as well as the combination of fludarabine with melphalan (100-140 mg/mg^2) Recipients of allogeneic hematopoietic cell transplantation (HCT) after either myeloablative or reduced intensity conditioning regimens; any donor source of stem cells is eligible Recipients of allogeneic hematopoietic cell transplantation (HCT) after either myeloablative or reduced intensity conditioning regimens; any donor source of stem cells is eligible Patients transplanted with hematopoietic stem cells from any source Peripheral blood stem cells must have been used as the stem cell source Donor must be willing to donate peripheral blood stem cells Peripheral blood stem cells, bone marrow, or umbilical cord blood may be used as the stem cell source Patients must have a related or unrelated peripheral blood stem cell donor as follows: Patient must not have received any prior marrow-ablative chemotherapy and autologous hematopoietic cell transplant Ineligible for hematopoietic stem cell transplant. Hematopoietic stem cell transplant =< 3 months prior to registration No prior hematopoietic transplant Prior hematopoietic transplant relapse within 1 year from frontline chemo-immunotherapy and ineligible for autologous hematopoietic stem cell transplant (auto-HSCT) History of organ or hematopoietic stem cell transplant. relapse within 1 year from frontline chemo-immunotherapy and ineligible for autologous hematopoietic stem cell transplant (auto-HSCT) Has received prior autologous hematopoietic stem cell transplant within the last 60 days Prior hematopoietic stem cell transplant for AML Be a recipient of hematopoietic stem cell transplant. Patients who are hematopoietic stem cell transplant candidates are excluded Prior hematopoietic stem cell transplant for the diagnosis of MDS Hodgkin's disease (HD): Induction failures, after first complete remission, or relapse (including relapse post autologous hematopoietic stem cell transplant), or those with active disease Patient must be ? 3 months from hematopoietic stem cell transplant, must not have active GVHD, and must be off all immunosuppression Patients must not have a prior autologous, syngeneic or allogeneic hematopoietic stem cell transplant Received a hematopoietic stem cell transplant within the previous 2 months Stem cells: patients must have an autologous hematopoietic stem cell product cryopreserved and available for re-infusion after 131I-8H9 treatment; the minimum dose for hematopoietic stem cells is 2 x 10^6 cluster of differentiation (CD)34+ cells/kg Stem cells from an identical donor could be used for autologous hematopoietic cell transplant (HCT) Prior hematopoietic cell transplant: must be >= 3 months after previous transplant History of, or scheduled, hematopoietic stem cell transplant within 24 weeks of Screening Hodgkin's disease (HD): induction failures, second or third complete remission, or relapse (including relapse post autologous hematopoietic stem cell transplant) Prior hematopoietic stem cell transplant The subject must be a recipient of hematopoietic stem cell or solid organ transplant. Hematopoietic cell transplant-co-morbidity Index greater than 2 Has no other hematopoietic stem cell transplant of any type prior to the current planned autologous hematopoietic cell transplant Has received any type of hematopoietic cell transplant Prior allogeneic or autologous hematopoietic stem cell transplant in the last 6 months Prior history of hematopoietic stem cell transplant Unless approved by the medical monitor, may not have received autologous hematopoietic stem cell transplant within 3 months before treatment Prior hematopoietic stem cell transplant. Considered eligible for hematopoietic stem cell transplant (allogeneic or autologous) at the time of signing the ICF. History of hematopoietic stem cell transplant Prior allogeneic hematopoietic stem-cell transplant for participants with DLBCL, FL, MCL, and CLL only. Prior allogenic hematopoietic stem-cell transplant is permitted for participants with ALL Received autologous hematopoietic stem cell transplant within the last 3 months Prior autologous hematopoietic stem cell transplant ? 3 months. Newly diagnosed, symptomatic multiple myeloma patients for whom treatment is indicated per the NCCN guidelines, and for whom a hematopoietic stem cell transplant is not planned or scheduled during the study or are considered ineligible for hematopoietic stem cell transplant, with measurable disease Received a hematopoietic stem cell transplant Non-Hodgkin's lymphoma - induction failures, second or third complete remission, or relapse (including relapse post autologous hematopoietic stem cell transplant) Hodgkin's disease - induction failure, second or later complete remission, or relapse (including relapse post autologous hematopoietic stem cell transplant) Hodgkin's disease (HD): induction failures, second or third complete remission, or relapse (including relapse post autologous hematopoietic stem cell transplant); or Prior autologous hematopoietic stem cell transplant Prior hematopoietic stem cell transplant Prior autologous hematopoietic stem cell transplant within 90 days of study entry Autologous hematopoietic stem cell transplant or fludarabine chemotherapy within 6 months of study enrollment Transformed lymphoma is included if patients are ineligible for (or refuse) hematopoietic stem cell transplant Has not received a prior hematopoietic stem cell transplant within the previous 3 months Patients who are candidates for hematopoietic stem cell transplant Prior treatment with hematopoietic stem cell transplant Prior autologous hematopoietic stem cell infusion <4 weeks prior to first study dose Prior autologous or allogeneic hematopoietic stem cell transplant Hematopoietic stem cell transplant recipient within 100 days post-transplant Patients must have received allogeneic hematopoietic stem cell transplant and be greater than 30 days post-transplant at the time of registration Prior allogeneic hematopoietic stem cell transplantation; (patients may have received a prior autologous hematopoietic stem cell transplant) Scheduled to undergo either autologous or allogeneic hematopoietic stem cell transplant Prior autologous or allogeneic hematopoietic stem cell transplant Planned post-transplant maintenance therapy except for FLT3 inhibitors or TKIs must be declared prior to randomization. If it is known prior to enrollment that the hematopoietic stem cell product will need to be cryopreserved, the patient should not be enrolled. Between 12 and 60 months after completion of cancer therapy (chemotherapy, radiation, hematopoietic cell transplant [HCT]) Prior allogeneic or autologous hematopoietic stem cell transplant in past 12 months Autologous hematopoietic stem cell transplant < 3 months prior to enrollment. Patients with prior autologous hematopoietic stem cell transplant who, in the investigator's judgment, have not fully recovered from the effects of the last transplant (e.g., transplant related side effects). Ages =< 50 years of age with hematologic diseases treatable by allogeneic HCT who through pre-existing medical conditions or prior therapy are considered to be at high risk for regimen related toxicity associated with a high dose transplant (> 40% risk of transplant-related mortality [TRM]); this criterion can include patients with a HCT-comorbidity index (CI) score of >= 1; transplants should be approved for these inclusion criteria by the principal investigators at the collaborating centers and at Fred Hutchinson Cancer Research Center (FHCRC); all children < 12 years must be discussed with the FHCRC principal investigator (PI) prior to registration Patients with short life expectancy (less than 3 months) due to comorbidity other than MDS or CMML Age-adjusted hematopoietic cell transplantation-comorbidity index (aaHCT-CI) less than or equal to 7. Patients >= age 50 must have an comorbidity score (hematopoietic cell transplant-comorbidity index [HCT-CI]) =< 4 (Sorror). The principal investigator is the final arbiter for comorbidity; Hematopoietic stem cell transplant comorbidity index (HCT-CI) >= 3^50 Ages =< 50 years of age with hematologic diseases treatable by allogeneic HCT who through pre-existing medical conditions or prior therapy are considered to be at high risk for regimen related toxicity associated with a high dose transplant (> 40% risk of transplant related mortality [TRM]); this criterion can include patients with a hematopoietic cell transplant-comorbidity index (HCT-CI) score of > 3; transplants should be approved for these inclusion criteria by the principal investigators at the collaborating centers and at Fred Hutchinson Cancer Research Center (FHCRC); all children < 12 years must be discussed with the FHCRC principal investigator (PI) prior to registration Patients with short life expectancy (less than 3 months) due to comorbidity other than MDS Patients >= age 50 must have a comorbidity score (hematopoietic cell transplant-comorbidity index [HCT-CI]) < 4 (Sorror) > 5 comorbidity points on the Hematopoietic Cell Transplant Co-Morbidity Index (HCT CI) Patients aged 70-75 with hematopoietic cell transplant-co-morbidity index (HCT-CI) of 0-1 are eligible Patients with comorbidity score > 3; the principal investigator is the final arbiter of eligibility for comorbidity score > 3 Patients >= 70 and =< 75 years of age may be eligible if they have a Hematopoietic Cell Transplantation- Comorbidity Index (HCT-CI) Co-Morbidity score =< 2 at least 1 grade 4 CIRS-G comorbidity (if compatible to participation in the study). Patients with a life expectancy of < 6 months as predicted by the Adult Comorbidity Index (ACE-27) PART 2: Comorbidity Index < 5 at the time of pre-transplant evaluation Hematopoietic cell transplantation (HCT) co-morbidity index score > 3; the principal investigator is the final arbiter of eligibility for comorbidity score > 3 Hematopoietic Cell Transplantation-Specific Comorbidity Index score (HCT-CI) =< 4 for patients in Cohort 1 and > 4 for Cohort 2 Patients < age 60 years must have a Karnofsky performance status (KPS) of >= 80% and a hematopoietic cell transplant comorbidity index (HCT-CI) score of 5 or less Age >= 70 years AND/OR Charlson comorbidity index score >= 2 (prostate cancer diagnosis does not contribute to total score) Patients > 50 must have Karnofsky performance score >= 70 or ECOG 0-1 and comorbidity index < 5 Age ? 18 years with HCT comorbidity index < 3 Severe, active comorbidity, including any of the following: Patients > 45 to =< 65 years: Karnofsky >= 70 or ECOG 0-1 and non-age adjusted comorbidity index =< 5 Significant comorbidity associated with an estimation of < 5 remaining life years Patients must have a contraindication to cisplatin as defined in the following bullet points; sites must complete the online tool at comogram.org prior to step 1 registration to determine if the patient is eligible; the scores must be recorded on a case report form (CRF)\r\n* Age >= 70 with moderate to severe comorbidity or vulnerability to cisplatin, defined as having any one of the following conditions within 30 days prior to step 1 registration:\r\n** Modified Charlson Comorbidity Index >= 1\r\n** Adult Comorbidity Evaluation (ACE)-27 Index >= 1\r\n** Generalized Competing Event Model for Cancer Risk (GCE) omega PFS score < 0.60 \r\n** Geriatric screening (G-8) score =< 14\r\n** Cancer and Aging Research Group (CARG) toxicity score >= 30%\r\n** Cumulative Illness Rating scale for Geriatrics (CIRS-G) score >= 4 OR\r\n* Age < 70 with severe comorbidity or vulnerability to cisplatin, defined as having two or more of the following conditions within 30 days prior to step 1 registration \r\n** Modified Charlson Comorbidity Index >= 1\r\n** ACE-27 Index >= 1\r\n** GCE omega PFS-score < 0.60 \r\n** G-8 score =< 14\r\n** CARG Toxicity score >= 30%\r\n** CIRS-G score >= 4 OR\r\n* Age >= 18 with an absolute or relative contraindication to cisplatin, defined as one or more of the following within 30 days prior to Step 1 registration:\r\n** Creatinine clearance (CC) > 30 and < 60 cc/min; for this calculation, use the Cockroft-Gault formula\r\n** Zubrod performance status 2 prior to step 1 registration\r\n** Pre-existing peripheral neuropathy grade >= 1\r\n** History of hearing loss, defined as either: \r\n*** Existing need of a hearing aid OR \r\n*** >= 25 decibel shift over 2 contiguous frequencies on a pretreatment hearing test Comorbidity or incurrent illness Charlson index of comorbidity score =< 4 Comorbidity that would interfere with therapy Ineligible for intensification treatment due to age or significant comorbidity > 5 comorbidity points on the Hematopoietic Cell Transplantation-Specific Comorbidity Index (HCT-CI) Patients >= 45 years: comorbidity score of 5 or higher Ages =< 50 years of age with hematologic diseases treatable by allogeneic HCT who through pre-existing medical conditions or prior therapy are considered to be at high risk for regimen related toxicity associated with a high dose transplant (> 40% risk of transplant related mortality [TRM]); this criterion can include patients with a HCT-comorbidity index (CI) score of >= 1; transplants should be approved for these inclusion criteria by the principal investigators at the collaborating centers and at the Fred Hutchinson Cancer Research Center (FHCRC); all children < 12 years must be discussed with the FHCRC principal investigator (PI) prior to registration Hematopoietic Cell Transplantation Specific Comorbidity Index (HCT-CI) < 5 for age < 65, HCT-CI < 4 for age > 65 History of uncontrolled depression or other psychiatric comorbidity with psychosis Underlying structural brain abnormality or neurologic comorbidity. Subject has a modified hematopoietic cell transplant comorbidity index (HCT-CI) score ? 4 Active infection or chronic comorbidity that would interfere with therapy No intent to use myeloablative conditioning regimens. Participants must be recipients of an allogeneic bone marrow or stem cell transplantation with myeloablative or reduced intensity conditioning regimens Participants may receive either a myeloablative or a non-myeloablative (reduced-intensity) conditioning regimen Recipient of a myeloablative or non-myeloablative allogeneic hematopoietic stem cell transplant (HSCT):\r\n* Conditioning regimen to be prescribed at investigator’s discretion, but will be prospectively defined as myeloablative or non-myeloablative Patients that have undergone immunotherapy in combination with non-myeloablative chemotherapy Prior myeloablative transplant containing full dose TBI (greater than 8 Gray [Gy]) Any prior myeloablative transplant within the last 6 months Will undergo first allogeneic hematopoietic stem cell transplantation (HSCT) for their malignancy. Conditioning may have been either conventional myeloablative (MAC) or reduced intensity conditioning (RIC) Patients >= 12 years and < 55 years are also included if they are not candidates for myeloablative conditioning regimens due to comorbidities Any conditioning regimen (non-myeloablative, myeloablative, or reduced intensity) is acceptable. Diagnosis: Patients with disorders affecting the hematopoietic system that are inherited, acquired, or result from myeloablative treatment. Use of myeloablative conditioning regimen Recipients of allogeneic stem cell transplantation with myeloablative or non-myeloablative conditioning regimens; alternative donor transplants (umbilical cord blood and haploidentical) are allowed Less than 3 months since prior myeloablative transplant (if applicable); less than 6 months since prior autologous transplant (if applicable) Deemed to be not otherwise eligible for a myeloablative hematopoietic cell transplant; high risk characteristics for a myeloablative transplant include age > 60 years and a HCT comorbidity index > 3 Less than 3 months since prior myeloablative transplant Patients with HM who have undergone myeloablative systemic therapy are ineligible to participate in this study. Must be >= 3 months after prior myeloablative transplant, if applicable Patients with or without previous myeloablative autologous transplant First allogeneic hematopoietic stem cell transplantation (HSCT) using myeloablative conditioning (MAC), non-myeloablative (NMA), or reduced-intensity conditioning (RIC) preparative regimens. Prior myeloablative or non-myeloablative allogeneic hematopoietic stem cell transplant using either bone marrow or peripheral blood stem cells or single or double cord blood within 24 months. Prior myeloablative or non-myeloablative autologous or allogeneic hematopoietic stem cell transplant using the marrow, peripheral blood stem cells or single or double umbilical cord blood Patients ineligible to receive full myeloablative conditioning regimen for allogeneic hematopoietic progenitor cell transplant due to age or comorbidities Prior myeloablative or non-myeloablative allogeneic hematopoietic stem cell transplant using either bone marrow or peripheral blood stem cells or single or double cord blood within 18 months Patients with relapsed disease after prior allogeneic SCT (myeloablative or non-myeloablative) will be eligible if they meet all other inclusion criteria and:\r\n* Have experienced graft rejection (no evidence of donor cells by short tandem repeat (STR) analysis on 2 occasions separated by at least 1 month)\r\n* Have no active graft-vs-host disease (GVHD) and require no immunosuppression\r\n* Are more than 6 months from transplant Patients developing aGvHD after ablative or non-myeloablative or reduced intensity conditioning will be eligible Second hematopoietic cell transplant: Must be >= 3 months after prior myeloablative transplant Myeloablative transplant within the last 6 months If > 18 years old, prior myeloablative transplant within the last 6 months If =< 18 years old, prior myeloablative transplant within the last 6 months; if > 18 years old prior myeloablative allotransplant or autologous transplant Second BMT: must be >= 3 months after prior myeloablative transplant If =< 18 years old, prior myeloablative transplant within the last 6 months; if >18 years old prior myeloablative allotransplant or autologous transplant Patients are eligible 12 weeks after myeloablative therapy with autologous stem cell transplant (timed from start of vorinostat); patients must meet adequate bone marrow function definition post-myeloablative therapy; patients who received stem cell reinfusion following non-myeloablative therapy are eligible once they meet peripheral blood count criteria Prior myeloablative allotransplant Patients who have received yttrium (Y)-90 ibritumomab (Zevalin) or iodine (I)-131 tositumomab (Bexxar), as part of their salvage therapy are not eligible for myeloablative UCB transplant Myeloablative or non-myeloablative allogeneic hematopoietic cell transplantation No prior myeloablative therapy or hematopoietic cell transplantation Must be >= 3 months after prior myeloablative transplant, if applicable Has received prior allogeneic transplants or who are planned to undergo umbilical cord blood transplant, receive ex vivo T-cell-depleted hematopoietic stem cells (HSCs), received any in vivo T-cell depleting antibodies, or non-myeloablative conditioning. Applicable disease and eligible for myeloablative SCT Patients with relapsed disease after prior allogeneic SCT (myeloablative or non-myeloablative) will be eligible if they meet all other inclusion criteria and\r\n* Have no active graft-versus-host disease (GVHD) and require no immunosuppression\r\n* Are more than 6 months from transplant Recipients of 7-8/8 human leukocyte antigen (HLA) matched adult donor allogeneic stem cell transplantation with myeloablative or non-myeloablative conditioning regimens Patients with uncontrolled infections for whom myeloablative hematopoietic stem cell transplant (HCT) is considered contraindicated by the consulting infectious disease physician (upper respiratory tract viral infection does not constitute an uncontrolled infection in this context) Prior myeloablative transplant containing full dose TBI (greater than 8 Gy) Myeloablative or non-myeloablative allogeneic hematopoietic cell transplant Prior myeloablative transplant within previous 3 months of study enrollment Prior myeloablative transplant within the last 6 months Prior myeloablative or non-myeloablative allogeneic hematopoietic stem cell transplant using either bone marrow or peripheral blood stem cells or single or double cord blood within 24 months. Patients are eligible 12 weeks after myeloablative therapy with autologous stem cell transplant (timed from start of protocol therapy); patients must meet adequate bone marrow function definition post-myeloablative therapy; patients who received stem cell reinfusion following non-myeloablative therapy are eligible once they meet peripheral blood count criteria; patients status post-allogeneic stem cell transplant are excluded unless they are > 1 year post transplant, have been off all immunosuppressive therapy for more than 3 months and do not have active graft-versus-host disease (GVHD) Patients are eligible 12 weeks after date of autologous hematopoietic stem cell infusion following myeloablative therapy (timed from first day of this protocol therapy). Patients who have received an autologous hematopoietic stem cell infusion to support non-myeloablative therapy (such as 131I-MIBG) are eligible at any time as long as they meet the other criteria for eligibility. Donor cellular engraftment of at least 2.5% from the non-myeloablative procedure and prior to the first infusion Subjects who had histopathologically confirmed overall grade 4 GVHD lasting longer than 7 days, from the non-myeloablative therapy, are not eligible Acute lymphoblastic leukemia (ALL) \r\n * ALL patients will be eligible if they fail to attain an initial remission, if they relapse within 1 year following the discontinuation of chemotherapy, or if they have other unfavorable prognostic features such that a stem cell transplant (SCT) would offer a significant survival advantage; patients must be in complete remission or have =< 25% blasts in bone marrow at the time of admission to the HSCT unit; patients in complete remission will preferentially receive a myeloablative transplant from a related or unrelated donor; however, patients will be eligible for this study if a suitable related or unrelated donor cannot be identified, the amount of time required to identify a suitable donor is deemed unacceptable, or the patient is not eligible for a myeloablative transplant regimen\r\n * Patients who relapse following a myeloablative transplant, but cannot receive DLI (e.g. cord blood recipients, graft loss) will also be eligible; such patients must be >= 6 months post initial transplant, achieve a CR or have =< 25% blasts in the bone marrow prior to admission to the HSCT unit Meet standard criteria as defined by the institution for a myeloablative allogeneic stem cell transplantation, with myeloablative defined as using conditioning regimens containing:\r\n* Total-body irradiation (TBI) >= 1200 cGy, or \r\n* Busulfan >= 12.8 mg/kg Myeloablative preparative regimen (for SAA any conditioning therapy allowed) Conditioning Regimen: Patients expecting to receive any type of myeloablative HSCT conditioning regimen are eligible Between day +28 and day +42 status post myeloablative or nonmyeloablative UCBT (single or double cord blood transplant) Patients must be receiving a fractionated total body radiation (FTBI) based- myeloablative conditioning regimen; (acceptable conditioning regimens include total body irradiation [TBI] + cyclophosphamide or TBI + etoposide) All conditioning regimens will be eligible (in case of allogeneic HCT, patient could have received myeloablative or non-myeloablative/reduced-intensity conditioning) Prior myeloablative or non-myeloablative allogeneic hematopoietic stem cell transplant using either bone marrow or peripheral blood stem cells within 12 months Myeloablative preparative regimen (i.e., >= TBI 12.0 Gy, >= busulfan (BU) 8.0 mg/kg PO, >= BU 6.4 mg/kg intravenously (IV), >= treosulfan 42 g/m^2 IV) according to investigational study or standard treatment plan; other \myeloablative\ preparative regimens are acceptable as long as they are approved by the principal investigator or designee Less than 3 months from myeloablative conditioning for autologous transplantation Planned myeloablative conditioning regimen Patients who have undergone a non-myeloablative stem cell transplant must have > 80% donor hematopoiesis within 30 days of study enrollment; chimerism within 30 days of study entry must be greater than, equal to, or no more than 5% less than the chimerism measured at approximately day +30 (if performed) Patients who have undergone a non-myeloablative stem cell transplant must have > 65% donor lymphoid hematopoiesis within 30 days of study enrollment ELIGIBILITY FOR MYELOABLATIVE CONDITIONING Myeloablative preparative regimen Less than 3 months from myeloablative conditioning for autologous transplantation (if applicable) Be scheduled to receive one of 3 myeloablative conditioning regimens (defined in population) followed by allogeneic SCT for hematological malignancy. Clinically suspected Grade II to IV aGVHD as per MAGIC criteria, occurring after allo-HSCT and any GVHD prophylaxis regimen. Has received more than 1 allo-HSCT. Participants with evidence of relapsed primary disease, or participants who have been treated for relapse after the allo-HSCT was performed. Patients who received Allo-Stem cell Transplantation(Allo-SCT) within 12 months. Completed allogeneic stem cell transplant (allo-SCT) or are eligible for and willing to complete allo-SCT Any patients eligible for allogeneic stem cell transplantation (allo-SCT) and willing to undergo allo-SCT as determined at time of screening for trial; patients who are ineligible or not interested in undergoing allo-SCT will be eligible for the trial Patients who are receiving any other investigational agents, with the exception of virus-specific cytotoxic T-cells for the treatment of viral infection/reactivation prior to allo BMT PHASE I: For the post allo-HCT cohort, chimerism analysis must demonstrate > 95% either donor or recipient in peripheral blood CD3 cells, must be done within 1 month of enrollment (no mixed chimerism are eligible) Patients with Allo-SCT on active GVHD or immunosuppression therapy within 3 months prior to C1D1. Acceptable allogeneic stem cell donor with imminent plans to proceed with allo-SCT. Allo-HSCT within 90 days of leukapheresis Prior allo-HCT less than three months from the time of enrollment Previous allo-HSCT of any kind Allowed prior allogeneic hematopoietic stem cell transplantation (allo-HCT) regardless of stem cell source; patients must be at least 3 months post allo-HCT (at time of treatment start); mismatched transplantations would be allowed If post allo-HCT, then patient must have baseline donor T cell chimerism of >= 20% (from peripheral blood); evaluation can be made within 4 weeks of treatment start Acute Leukemia (AML or ALL) patient or allo-HCT recipient with a diagnosis of IA Prior allogeneic (allo)-hematopoietic cell transplantation (HCT) less than three months from the time of enrollment Previous allogeneic (allo)-transplant of any kind Has received more than 1 allo-HSCT. Subjects with evidence of relapsed primary disease, or subjects who have been treated for relapse after the allo-HSCT was performed. Unresolved toxicity or complications (other than acute GVHD) due to previous allo-HSCT. Received Janus kinase inhibitor therapy after allo-HSCT for any indication. Treatment with a JAK inhibitor before allo-HSCT is permitted. Inadequate recovery from toxicity and/or complications from the prior allo-HSCT. Patients underwent allo-SCT with intermediate risk and high risk AML and high risk MDS (defined by American Society for Blood and Marrow Transplantation [ASBMT] criteria), who are within 60 to 100 days after allo-SCT Prior AP, BC or allo-transplant Recipient of 1 allo-HSCT but not more than 1 allo-HSCT. Relapse of underlying malignant disease after allo-HSCT. For Pre-allo Part A (before stem cell transplant): Relapsed or refractory AML (greater than 5% blasts) For Post-allo Part B: Treatment must begin at least 60 days, but no more than 100 days post-transplant. For Pre-allo Part A (before stem cell transplant): Prior alloSCT For Post-allo Part B: Active GVHD Grade 2 or higher For Post-allo Part B:History of veno-occlusive disease requiring defibrotide For Post-allo Part B: History of Grade 2 or higher hepatic GVHD A patient is eligible for second enrollment (allo-cellular therapy) if all of the following inclusion criteria are met: At least a partial remission before allo-SCT Patients undergoing their first T-cell replete allogenic (allo)-HCT for CLL, MCL, follicular lymphoma (FL), Hodgkin disease (HD) Patient undergoing an allo-SCT Planned to undergo allo-HSCT