Grade ? 2 graft-versus-host disease (GvHD) per the Center for International Blood and Marrow Transplant Research (CIBMTR) consensus grading system at enrollment Clinically significant graft versus host disease (GVHD) or GVHD requiring initiation of treatment or treatment escalation within 21 days, and/or > grade 1 persistent or clinically significant non-hematologic toxicity related to HSCT Allogenic or autologous transplant for hematological malignancy with infusion of stem cells within 90 days before Cycle 1 Day 1, or on active immunosuppressive therapy for graft-versus-host disease (GVHD) or GVHD prophylaxis within 2 weeks of Cycle 1 Day 1. Subject has active clinically significant graft versus host disease (GVHD) or is on treatment with systemic corticosteroids for GVHD (except grade 1 skin GVHD). At least 3 months must have elapsed since completion of allogeneic stem cell transplantation. Graft-versus-host disease (GVHD) prophylaxis with any of the following agents: calcineurin inhibitor, short-course methotrexate steroids, mycophenolate mofetil, and sirolimus Must be off all immunosuppressive medications (except steroids) for graft versus host disease (GVHD) for at least 2 weeks prior to study entry Patients must be free from active graft versus host disease (GVHD) and off immunosuppressive GVHD therapy for 4 weeks prior to enrollment At least 90 days have elapsed since bone marrow transplant and participant is off immune suppression for ? 2 weeks, if applicable with no evidence of active graft versus host disease (GVHD) Patients with active graft-versus-host-disease (GVHD) status post stem cell transplant, i.e. patients requiring therapy more than chronic steroid immunosuppression and/or phototherapy for chronic skin GVHD will be excluded. Requirement for systemic immunosuppressive therapy (e.g. graft-versus-host disease [GVHD] therapy within 12 weeks before the first dose of study drug) Chronic graft versus host disease (GVHD) or on immunosuppressive therapy for the control of GVHD; Subjects with active graft-vs-host disease (GVHD) requiring steroids or other immunosuppressive agents; history of >= grade II acute GVHD or extensive chronic GVHD Requirement for systemic immunosuppressive therapy (e.g. graft-versus-host disease [GVHD] therapy within 12 weeks before the first dose of study drug) Patients must be free from active graft versus host disease (GVHD) and off immunosuppressive GVHD therapy for 4 weeks prior to enrollment Patients who have undergone allo-stem cell transplant (SCT) are eligible if they are at least 3 months post SCT, have relapsed AML, are not on treatment or prophylaxis for graft versus host disease (GVHD), and have no active GVHD. Active graft-versus-host disease (GvHD), grade 2-4 according to the Glucksberg criteria, active chronic GvHD requiring systemic treatment or requirement for GvHD prophylaxis with cyclosporine or tacrolimus. Active graft versus host disease (GVHD) or on immunosuppressive medication of GVHD Patients with hematologic malignancies status post allogeneic SCT without evidence of disease relapse, active graft versus host disease (GVHD) or history of more than stage I skin acute GVHD; and off immunosuppression for at least 4 weeks; at least 60 days after allo-SCT Patients who are < 90 days post allogeneic stem cell transplant will be excluded; patients beyond 90 days post-allogeneic stem cell transplant with active uncontrolled graft versus host disease (GVHD) > grade 1 will be excluded; patients who are on a stable dose of immunosuppressive therapy (tacrolimus, cyclosporine, or other) for > 2 weeks will be eligible but those with recent increase in the immunosuppressive medication dose within last 2 weeks to control GVHD will not be included; Note: subjects may be using systemic corticosteroids or topical or inhaled corticosteroids post allogeneic stem cell transplant; patients requiring >= 1 mg/kg prednisone for GVHD management at the time of screening will not be eligible until the prednisone can be weaned to < 1 mg/kg; such patients should be monitored for at least 14 days and if no flare of GVHD requiring re-escalation of steroids or additional interventions for the GVHD they will be eligible No active graft-versus-host disease (GVHD) or on immunosuppressive medication for GVHD Patients who have received any systemic corticosteroid therapy within 4 weeks prior to the start of therapy, or 12 weeks if given to treat graft versus host disease (GVHD), with the exception of physiological replacement doses of cortisone acetate or equivalent Prior allogeneic transplant with graft-versus-host disease (GVHD) requiring ongoing immunosuppressive therapy < grade 2 acute graft versus host disease (GVHD) at time of the first NK cell-enriched DLI; patients with treated acute GVHD must be on a stable dose of therapy (no increase in immunosuppressive therapy for the 2 weeks before planned NK cell-enriched DLIs); the dosage/level of immunosuppressive therapy at the time of NK-DLIs should be no greater than 20mg of prednisone daily or mycophenolate 500 mg bid daily or cyclosporine with a target level of 200 ng/mL or tacrolimus with a target level of 10 ng/ml Patients must have no evidence of active graft-versus-host disease at the time of the CD8+ memory T-cell infusion; patients with a history of acute GVHD overall grade II based on skin only involvement or upper gastrointestinal (GI) tract involvement only will be eligible; patients with a history of liver or lower GI tract GVHD will not be eligible Acute graft-versus-host disease (GVHD) ? Grade 1, either no signs of chronic GVHD or mild chronic GVHD graded as limited disease Receipt of hematopoietic stem cell transplant (HSCT) within 60 days of the first dose of TAK-659; clinically significant graft-versus-host disease (GVHD) requiring ongoing immunosuppressive therapy post HSCT at the time of screening (use of topical steroids for ongoing skin GVHD is permitted). Patients with chronic graft-versus-host disease (GVHD) if on prednisone equal to or less than 0.5 mg/kg and not receiving second-line GVHD treatments like pentostatin, infliximab, etanercept, etc Prior allogeneic transplant with graft-versus-host disease (GVHD) requiring immunosuppressive therapy No active graft versus host disease (GVHD) or immunosuppression for prevention or treatment of GVHD within two weeks of study entry No active graft versus host disease (GVHD): patients with a history of stem cell transplant are eligible but cannot have evidence of active GVHD as determined by the investigator Patients with active (grade 2-4) acute graft vs. host disease (GVHD), chronic GVHD or an overt autoimmune disease (e.g. hemolytic anemia) requiring high doses of glucocorticosteroid (> 0.5 mg/kg/day prednisone or its equivalent) as treatment Patients with active (grade 2-4) acute graft versus host disease (GVHD), chronic GVHD, or an overt autoimmune disease (e.g. hemolytic anemia) requiring glucocorticosteroid treatment (> 0.5 mg/kg/day prednisone or its equivalent) as treatment Grade 3 or higher Graft Versus Host Disease (GVHD), or GVHD on either a calcineurin inhibitor or prednisone more than 5 mg/day. Have clinically significant graft versus host disease (GVHD), or GVHD requiring initiation or escalation of treatment within the last 21 days greater than 5 years ago but has active graft versus host disease (GvHD) requiring systemic treatment. Clinically significant graft versus host disease (GVHD) or active GVHD requiring initiation or escalation of treatment within 28-day screening period. any active acute graft versus host disease (GvHD), grade 2- 4, according to the Glucksberg criteria or active chronic GvHD requiring systemic treatment Graft-Versus-Host Disease (GVHD) therapy within 6 weeks before the first dose of study drug; low dose steroids (? 10mg) allowed Recipients of previous allogeneic transplants who have rash involving more than 10% body surface area attributed to graft versus host disease (GVHD) (> grade 1 GVHD of skin); stem cell transplant recipients will be excluded if they are still receiving immunosuppression including steroids for GVHD or have active GVHD in any organ (except for grade 1 only of skin, not requiring treatment) Active, uncontrolled graft vs. host disease (GVHD) following allogeneic transplant for non-AML condition (e.g. MDS, lymphoid malignancy, aplastic anemia); patients with GVHD controlled on stable doses of immunosuppressants are eligible Patients with an allogeneic transplant must meet the following conditions: the transplant must have been performed more than 90 days before registration to this study, the patient must not have >= grade 2 acute graft versus host disease (GvHD) or either moderate or severe limited chronic GvHD, or extensive chronic GvHD of any severity; the patient must be off all immunosuppression for at least 2 weeks Clinically significant graft versus host disease (GVHD) or GVHD requiring initiation of treatment or treatment escalation within 21 days, and/or > Grade 1 persistent or clinically significant non hematologic toxicity related to HSCT. Subjects who have undergone hematopoietic stem cell transplant (HSCT) within 60 days of the first dose of AG-120, or subjects on immunosuppressive therapy post HSCT at the time of screening, or with clinically significant graft-versus-host disease (GVHD). (The use of a stable dose of oral steroids post HSCT and/or topical for ongoing skin GVHD is permitted.) The patient is receiving immunosuppressive therapy - with the exception of low-dose prednisone (? 10 mg/day) - for treatment or prophylaxis of graft-versus-host disease (GVHD). If the patient has been on immunosuppressive treatment or prophylaxis for GVHD, the treatment(s) must have been discontinued at least 14 days prior to study treatment and there must be no evidence of Grade ? 2 GVHD. Active graft versus host disease (GVHD) ? Grade 2 or extensive chronic GVHD requiring immunosuppressive therapy EXCLUSION FOR TREATMENT: Patients with active (grade 2-4) acute graft versus host disease (GVHD), chronic GVHD or an overt autoimmune disease (e.g. hemolytic anemia) following allo-HSCT requiring glucocorticosteroid treatment (> 0.5 mg/kg/day prednisone or its equivalent) as treatment Systemic immunosuppressive therapy post HSCT or with clinically significant graft-versus-host disease (GVHD). Has chronic graft versus host disease (GVHD) or on immunosuppressive therapy for the control of GVHD Subjects who have undergone hematopoietic stem cell transplant (HSCT) within 60 days of the first dose of AG-221, or subjects on immunosuppressive therapy post HSCT at the time of screening, or with clinically significant graft-versus-host disease (GVHD). (The use of a stable dose of oral steroids post GVHD and/or topical steroids for ongoing skin GVHD is permitted with Medical Monitor approval.) Evidence of on-going graft versus-host disease (GVHD), or GVHD requiring immunosuppressive therapy Patients with active (grade 2-4) acute graft versus (vs.) host disease (GVHD), chronic GVHD or an overt autoimmune disease (e.g. hemolytic anemia) requiring high doses of glucocorticosteroid (> 0.5 mg/kg/day prednisone or its equivalent) as treatment Active graft versus host disease (GVHD) with other than grade 1 skin involvement or GVHD requiring immunosuppressive treatment. Newly diagnosed acute graft-versus-host disease (GvHD), including lower Gastrointestinal (GI) involvement (modified International Bone Marrow Transplant Registry [IBMTR] Severity Stage 1 to 4 [>500 mL diarrhea/day]), with or without other organ system involvement. Able to be off prednisone or other immunosuppressive medications for at least 3 days prior to Day 0 (excluding pre-medications); low dose prednisone (< 10 mg/day) is allowed if for indication other than graft-versus-host disease (GVHD) < 60 days from ASCT; has chronic graft-versus host disease (GVHD) or requires continued treatment with systemic immunosuppressive agents Clinically active or unstable graft-versus-host disease (GvHD) requiring treatment which precludes administration of chemotherapy as defined in this protocol Patients is off or on a stable dose of immunosuppressive drugs for management or prophylaxis of graft-versus-host disease (GVHD) (defined as no escalation of therapy for GVHD) within 14 days prior to starting crenolanib Active acute or extensive chronic graft-versus-host disease (GvHD) which included the administration of immunosuppressive agents to prevent or treat GvHD within 2 weeks before blinatumomab treatment Allogeneic stem cell transplant within 60 days, active acute or chronic graft-versus-host disease (GvHD), or receiving immunosuppressive therapy as treatment for GvHD Grade ? 2 graft-versus-host disease (GvHD) per the Center for International Blood and Marrow Transplant Research (CIBMTR) consensus grading system at enrollment For both Parts 1 and 2, receipt of HSCT within 60 days of the first dose of PLX3397 is an exclusion criterion. Patients on immunosuppressive therapy post HSCT, or with clinically significant graft-versus-host disease are excluded from Part 1. (Use of topical steroids for ongoing skin GVHD is permitted). Patients for Part 1 must have a wash-out period of ?2 weeks or at least 4 half-lives from their last systemic immunosuppressive treatment for GVHD. Patients for Part 2 may be receiving systemic immunosuppressive treatment for management of GVHD at the time of screening and enrollment =< grade 1 acute graft-versus-host disease (GVHD) at time of the CMV specific T cell infusion; patients with treated acute GVHD must be on a stable dose of therapy (no increase in immunosuppressive therapy for the 2 weeks before planned donor cell infusion); the dosage level of immunosuppressive therapy at the time of infusion should be no greater than 20 mg of prednisone daily or mycophenolate 1000 mg thrice daily (TID) or cyclosporine with a target level of 200 ng/ml or equivalent For patients who have received prior HSCT, there can be no evidence of graft versus host disease (GVHD) and greater than 60 days must have elapsed since the HSCT Patients with active, grade II-IV, acute graft versus (vs.) host disease (GVHD), chronic GVHD or any condition requiring high doses of glucocorticosteroid (> 0.5 mg/kg/day prednisone or its equivalent) as treatment Patients with chronic, severe, generalized skin breakdown (such as generalized blistering, burns, severe graft versus host disease [GVHD] with open sores, etc.) are ineligible If patients are on immunosuppressive therapy for treatment of graft versus host disease (GVHD), then only those on stable doses for at least 4 weeks (or on tapering doses) will be eligible If patients are on immunosuppressive therapy for treatment of graft versus host disease (GVHD), then only those on stable doses for at least 4 weeks (or on tapering doses) will be eligible Planned graft versus host disease (GVHD) prophylaxis consisting of tacrolimus (TAC)/methotrexate (MTX) or TAC/sirolimus (SRL) The patient underwent autologous or allogeneic stem cell transplant within 60 days prior to receiving the first dose of omacetaxine and has any evidence of ongoing graft versus host disease (GVHD), or GVHD requiring immunosuppressive therapy. Subjects on systemic immunosuppressive therapy post HSCT at the time of screening, or with clinically significant graft-versus-host disease (GVHD). The use of topical steroids for ongoing skin or ocular GVHD is permitted. Allogeneic stem cell transplantation is allowed provided the patient is >= 1 year from transplant at time of registration, is not on immunosuppressive therapy to treat/prevent graft-versus-host disease, has no evidence of active graft versus host disease, and no evidence of active infection At least 3 months from allogeneic stem cell transplantation and off immunosuppression and no evidence of graft versus host disease (GVHD) Prior allogeneic stem cell transplantation with active graft-versus-host-disease. Patients with a history of allogeneic stem cell transplantation are eligible for study participation provided the transplant was > 100 days prior to the first dose of treatment on study; patients must be off of immunosuppressive therapies for at least 4 weeks prior to the first dose of treatment on study without signs or symptoms of graft versus host disease other than grade 1 skin involvement Patients who have undergone stem cell transplantation (SCT), autologous or allogeneic, are eligible provided that they are >= 8 weeks from stem cell infusion, have no active graft versus host disease (GVHD), are off immune suppression for at least 2 weeks, and do not have a history of veno-occlusive disease (VOD) Patients with history of allogeneic stem cell transplantation are eligible if at least 100 days post-transplant, if there is no evidence of active graft versus host disease (GVHD) and no longer taking immunosuppressive agents for at least 30 days prior to enrollment Prior allogeneic stem cell transplantation (SCT) is an exclusion only if the subject has active graft vs host disease or requires immunosuppression other than a constant stable dose of glucocorticoids (the latter is permitted) Prior allogeneic stem cell transplantation with active graft-versus-host- disease High risk prediction score as determined by the Mount Sinai Acute Graft Versus Host Disease (GVHD) International Consortium (MAGIC) algorithm at either day 7 or day 14 post hematopoietic stem cell transplantation (HCT). Patients with history of allogeneic stem cell transplantation are eligible if at least 100 days post-transplant, if there is no evidence of active GVHD and no longer taking immunosuppressive agents for at least 30 days prior to enrollment In subjects with prior hematopoietic progenitor cell transplantation, evidence of ongoing graft-versus-host disease (GVHD). AML relapse > 6 months since autologous or allogeneic stem cell transplantation, provided there is no active graft-versus-host disease (GVHD) > grade 1; no treatment with high dose steroids for GVHD (up to 20 mg prednisolone or equivalent); no treatment with immunosuppressive drugs with the exception of low dose cyclosporine and tacrolimus (blood levels of 0.5-0.6 ug/mL) Meets one of the following disease criteria:\r\n* Multiple myeloma (MM) meeting one of the following:\r\n** Relapsed/refractory disease after two lines of therapies, including a proteasome inhibitor (bortezomib, carfilzomib or ixazomib) and an immunomodulatory drug (thalidomide, lenalidomide or pomalidomide)\r\n** Relapsed disease between 2-18 months of 1st autologous stem cell transplantation\r\n** Relapsed disease at least 4 months after allogeneic stem cell transplantation with no evidence of active graft versus host disease AND with measurable disease defined as serum IgG, A, M M-protein >= 0.5 g/dL or serum IgD M-protein >= 0.5 g/dL, or urine M-protein >= 200 mg/24 hours AND at least at least 4 weeks since plasmapheresis\r\n* CD20-positive B-cell non-Hodgkin lymphoma (NHL)\r\n** CD20 expression confirmed by flow cytometry or immunohistochemistry and meeting one or more of the following:\r\n** Evidence of relapsed/refractory disease that has failed conventional therapy\r\n** Relapsed disease at least 60 days after autologous stem cell transplantation\r\n** Relapsed disease at least 4 months after allogeneic stem cell transplantation with no evidence of active graft versus host disease\r\n** Has measurable disease > 1.5 cm in diameter Patients with prior autologous or allogeneic hematopoietic cell transplantation (HCT) are eligible if relapse occurs provided symptoms of graft-versus host disease are well controlled with stable use of immunosuppressive agents Patients who have had prior SCT are eligible if they have a relapse > 3 months since autologous or allogeneic stem cell transplantation provided, 1) no clinically significant active graft-versus-host disease (GVHD > grade 1); 2) no treatment with high dose steroids for GVHD (i.e. > 20 mg prednisolone or equivalent per day); 3) no treatment with immunosuppressive drugs with the exception of cyclosporine and tacrolimus Patient participants who have undergone allogeneic SCT (alloSCT) are eligible if they are >= 60 days from stem cell infusion, have no evidence of graft versus host disease (GVHD) > grade 1, and are >= 2 weeks off all immunosuppressive therapy Chronic graft-versus-host disease requiring systemic immunosuppression post-allogeneic hematopoietic stem cell transplantation Patients who have undergone stem cell transplantation (SCT), autologous or allogeneic, are eligible provided that they are > 60 days from stem cell infusion, have graft-versus-host disease (GVHD) =< grade 1 and are off immunosuppressive agents for > 28 days at time of registration Patient must meet one of the following criteria: \r\n* Patient refractory to one or two standard induction regimen \r\n* Patients with a first untreated relapse within 2 years of documentation of clinical remission; patients relapsing after allogeneic stem cell transplantation are eligible if more than 12 months after transplantation and without sign of active graft versus host disease (GVHD) Patients with prior autologous and allogeneic hematopoietic stem cell transplantation are eligible if patients are off immunosuppression for greater than 14 days and have no evidence of active graft versus host disease (GVHD) except grade 1 skin GVHD Prior allogeneic transplants is allowed prior to study start (1st dose of study medication), but patients must also be at least 6 months from date of stem cell infusion, have no evidence of graft versus host disease (GVHD), be off all immunosuppressant medications, and have recovered to =< grade 1 toxicities related to this procedure Relapse > 6 months since autologous or allogeneic stem cell transplantation provided:\r\n* No active graft-versus-host disease (GVHD > grade 1)\r\n* No treatment with high dose steroids for GVHD (up to >= 20 mg prednisolone or equivalent per day)\r\n* No treatment with immunosuppressive drugs with the exception of low dose cyclosporine and tacrolimus Patients with relapsed or primary refractory AML; patients with relapsed AML after allogeneic stem cell transplantation, including those who have received donor lymphocyte infusions, are eligible if they have no active graft versus host disease (GVHD) and are off immunosuppression Patients having undergone prior allogeneic stem cell transplantation within 6 months or having active graft versus host disease. Previous allogeneic stem cell transplantation with active graft versus host disease (GVHD), or treatment with immunosuppressive therapy (excluding corticosteroids) in the 2 months prior to study entry Patients who have undergone allogeneic SCT (alloSCT) are eligible if they are >= 60 days post stem cell infusion, have no evidence of graft-versus-host disease (GVHD) > grade 1, and are >= 2 weeks off all immunosuppressive therapy Patients with history of allogeneic stem cell transplantation are eligible if at least 100 days post-transplant, if there is no evidence of active graft-versus-host disease (GVHD) and no longer taking immunosuppressive agents for at least 30 days prior to enrollment Prior hematopoietic stem cell transplantation within 12 weeks of the first dose of study treatment or ongoing immunosuppressive therapy for graft versus host disease Patients who have received allogeneic hematopoietic stem cell transplantation will be eligible 6 months after the procedure provided there is no evidence of active graft-versus-host disease and immunosuppressive treatment has been discontinued for at least 30 days. Patients with allogeneic stem cell transplantation within the last 6 months or patients with active graft-versus-host disease (GVHD) will be excluded For patients with relapsed/refractory disease: patients with prior autologous or allogeneic hematopoietic cell transplantation (HCT) for MDS/AML are eligible if relapse occurs provided symptoms of graft-versus host disease are well controlled with stable use of immunosuppressive agents Active graft versus host disease (GVHD) after allogeneic stem cell transplantation; at least 2 months must have elapsed since completion of an allogeneic stem cell transplantation Patients who have received allogenic stem cell transplantation < 12 months prior to entering the study or show evidence of active graft-versus-host disease that requires immunosuppressive therapy Patients who have undergone stem cell transplantation (SCT), autologous or allogeneic, are eligible provided that they are > 84 days from stem cell infusion, have no active graft-versus-host disease (GVHD), are off immunosuppressive agents for > 14 days Participants who have had prior allogeneic stem cell transplantation with evidence of active graft-versus-host disease requiring immunosuppressive therapy Recipients of prior allogeneic hematopoietic stem cell transplantation for AML or acute leukemia of ambiguous lineage are eligible if they do not have graft-versus-host disease (GVHD) or they have quiescent GVHD whether or not they are receiving immunosuppressive therapy Patients must have no evidence of active graft-versus-host disease and must be on a stable immunosuppressive regimen (or no immunosuppressive medications) without a change in drugs dosage in the 4 weeks prior to the planned CD8+ memory T cell infusion Patients who have undergone prior stem cell transplantation will not be excluded from study entry; at least 3 months must have elapsed since autologous or allogeneic stem cell transplantation; patients must have no evidence of active graft versus host disease Patients with prior autologous and allogeneic hematopoietic stem cell transplantation are eligible if patients are off immunosuppression for > 1 month and have no evidence of active graft versus host disease (GVHD) except grade 1 skin GVHD Any evidence of ongoing graft-versus-host disease (GVHD) in subjects with prior progenitor cell transplantation; Patients following allogeneic stem cell transplantation are eligible in the absence of graft versus host disease and are off immunosuppression for at least 30 days Allogeneic stem cell transplantation within the last 28 days before first treatment with graft versus host disease requiring more than 20 mg of steroids per day. Steroid dosage must be stable within two weeks prior to start of treatment. AML relapse > 6 months since autologous or allogeneic stem cell transplantation, provided they are in first or second relapse and: No active graft-versus-host disease (GVHD > grade 1). No treatment with high dose steroids for GVHD (up to 20 mg Prednisolone or equivalent, Appendix G). No treatment with immunosuppressive drugs with the exception of low dose cyclosporine and tacrolimus (blood levels of 0.5-0.6 µg/mL). Patients with prior autologous or allogeneic hematopoietic cell transplantation (HCT) are eligible if relapse occurs provided symptoms of graft-versus host disease are well controlled with stable use of immunosuppressive agents Patients who have had prior allogeneic stem cell transplantation and show evidence of active graft-versus-host disease that requires immunosuppressive therapy Patients with active graft versus host disease after allogeneic stem cell transplantation. At least 3 months must have elapsed since completion of allogeneic stem cell transplantation except for patients with AML, where at least 2 months must have elapsed; Active graft versus host disease (after allogeneic stem cell transplantation) at C1D1. Adult HCT survivors as defined by being at least 100 days post autologous or allogeneic transplantation for a malignant disease; all hematologic malignancies will be included; there is no restriction to enrollment by donor type, donor cell source, presence or absence of graft versus host disease Active graft versus host disease (after allogeneic stem cell transplantation) at C1D1. Patients who have undergone prior allogeneic transplantation are eligible provided they do not have significant active graft versus host disease and that their transplant day 0 is > 6 months from their first dose of chemotherapy Prior allogeneic hematopoietic cell transplantation (HCT) with active graft versus host disease (GVHD) on therapeutic dosing of immunosuppression or prednisone > 20 mg daily equivalent Patients with a history of allogeneic hematopoietic stem cell transplantation (HSCT) will be eligible if they are more than 90 days removed from the date of stem cell infusion, have no evidence of acute graft-versus-host disease (GVHD) or active chronic (grade 2-4) GVHD, and are off of all transplant-related immunosuppression for at least 2 weeks Stem cell Infusion without TBI: no evidence of active graft vs host disease and at least 84 days must have elapsed after transplant or stem cell infusion No evidence of active graft versus (vs.) host disease and >= 2 months must have elapsed since transplant Stem cell transplant or rescue: no evidence of active graft versus (vs.) host disease and ? 2 months must have elapsed since transplant prior to registration No evidence of active graft versus host disease and >=2 months must have elapsed since transplant or rescue Stem Cell Transplant or Rescue: No evidence of active graft vs. host disease and ? 2 months must have elapsed since transplant. Hematopoietic cell transplant or other cellular based therapy within 30 days before the planned start of study treatment or patients with active graft-vs-host disease with the exception of Grade 1 skin involvement Presence of graft-vs-host disease (GVHD) No evidence of active graft vs. host disease and at least 2 months must have elapsed since transplant The patient must have no evidence of active graft vs. host disease, and greater than or equal to 12 weeks must have elapsed since transplant or stem cell infusion and enrollment on this study for any other pathology No evidence of active graft vs. host disease and at least 84 days must have elapsed after transplant or stem cell infusion. Stem Cell Transplant or Rescue: No evidence of active graft vs. host disease and ? 2 months must have elapsed since transplant. Patients may have had a prior stem cell transplant (autologous or allogeneic), however they may not have active graft-vs-host disease (GvHD), nor be on any immunosuppression Stem cell transplant or rescue: >= 2 months must have elapsed since the time of transplant; patients with active graft-vs-host disease (GVHD) are eligible if the disease is well controlled on GVHD medications and they are clinically stable Stem cell infusion without TBI: no evidence of active graft vs. host disease and at least 84 days must have elapsed after transplant or stem cell infusion Bone marrow/stem cell transplant or infusion without TBI:\r\n* Part A1 or Part C: No evidence of active graft vs host disease and >= 3 months must have elapsed since stem cell transplant or infusion\r\n* Part A2, Part A3, or Part B: No evidence of active graft vs host disease and >= 6 weeks must have elapsed since stem cell transplant or infusion Prior allogeneic stem cell transplant within one year or active graft vs. host disease. No evidence of active graft vs host and <3mo since Stem Cell Transplant Graft vs. host disease following prior allogeneic transplant within 3 months prior to study treatment. Allogeneic transplant within 30 days prior to the planned start of treatment or subjects with active graft-vs-host disease with the exception of Grade 1 skin involvement Patient must be:\r\n* >= 6 months since allogeneic bone marrow transplant prior to enrollment\r\n* >= 3 months since autologous bone marrow/stem cell prior to enrollment\r\n* >= 3 months since stem cell transplant or rescue without TBI with no graft vs. host disease prior to enrollment\r\n* No graft versus host disease Ongoing graft-vs-host disease Autologous stem cell transplant or rescue: No evidence of active graft versus (vs.) host disease and >= 4 weeks must have elapsed Ongoing graft-vs-host disease Prior bone marrow transplant presenting with active uncontrolled graft versus (vs.) host disease (GVHD) Prior bone marrow transplant that requires immunosuppressant therapy or presents with graft vs host disease (GVHD). Patient must be:\r\n* >= 6 months since allogeneic bone marrow transplant prior to registration\r\n* Stem cell transplant or rescue without TBI: no evidence of active graft versus (vs) host disease and >= 3 months must have elapsed since transplant Previous allogeneic stem cell transplant is allowed only if subjects are >100 days from stem cell transplant and do not have uncontrolled acute or chronic graft-vs-host disease There is no evidence of active graft vs host disease Ongoing graft-vs-host disease. Ongoing graft-vs-host disease patients with Stem Cell Transplant (SCT) or Rescue without TBI: Evidence of active graft vs. host disease and < 3 months since SCT Stem Cell Transplant or Rescue: No evidence of active graft vs. host disease and >= 2 months must have elapsed Non-manageable graft versus host disease. Active graft-versus-host disease. Active graft-versus-host disease. Participants must have cGVHD (as defined by the National Institutes of Health Consensus Development Project on Criteria for Clinical Trials in Chronic Graft-Versus-Host Disease) Current or history of graft versus host disease Active chronic graft versus host disease requiring immunosuppressive treatment. Patients with >= grade 3 acute graft-versus-host disease are excluded from the study Patients with moderate or severe chronic graft-versus host requiring more than 20 mg of oral prednisone or equivalent therapy are excluded from the study Patients who have undergone allogeneic stem cell transplant > 12 months, without active graft-versus-host-disease, and not on immunosuppression for prevention of graft-versus-host disease are eligible there are no signs or symptoms of graft versus host disease, other than Grade 1 skin involvement. GRAFT CRITERIA: No prior therapy with mTOR inhibitors except for rapalog treatment as part of graft-versus-host (GVH) prophylaxis or treatment Graft must be a CD3+ T-cell replete PBSC graft or non-manipulated BM graft. Presence of chronic graft versus host disease (cGVHD) in an organ other than lung Active graft-versus-host disease. Active hepatic graft-versus-host disease Active graft versus-host disease and must not be on immunosuppression Participants who have received immunosuppressive therapy for graft versus host disease within 2 weeks prior to randomization Any level of acute graft versus host disease GRAFT CRITERIA: DONOR: Donors will be selected to minimize HLA mismatch in the host-versus-graft direction Active acute graft-versus-host disease of any grade or chronic graft-versus-host disease of Grade 2 or higher Less than 3 months since received hematopoietic stem cell transplantation, autologous or allogeneic and/or have clinically significant graft versus-host disease requiring treatment at the time of screening and/or patient having a history of severe graft versus-host disease; Signs of or symptoms of active graft versus host disease Patients with symptomatic oral chronic graft-versus-host disease (sensitivity score >= 4) Graft-versus-host disease criteria: Active graft-versus-host disease. Active graft-versus-host disease. Active acute grade III-IV graft-versus-host disease Ongoing graft-versus-host disease Prior use of fludarabine, as this agent has been associated with higher subsequent rates of graft versus host disease Active graft?versus?host disease requiring systemic treatment Patients who have undergone allogeneic stem cell transplant within 12 months, without active graft-versus-host-disease, and not on immunosuppression for prevention of graft-versus-host disease are eligible Subjects who have clinically significant graft versus host disease requiring treatment and /or have >grade 2 persistent non hematological toxicity related to transplant Participants who received prior allogenic transplant must have had no active graft-versus-host disease. Active graft versus host disease. Presence of uncontrolled graft-versus-host disease Evidence of graft versus host disease > grade II Evidence of chronic or acute graft versus host disease or on-going treatment for graft versus host disease from prior allogeneic stem cell transplantation Current immunosuppressive treatment for graft versus host disease Active graft versus host disease No signs or symptoms of graft versus host disease other than Grade 1 skin involvement Has clinically significant graft-versus-host disease requiring treatment Ongoing graft-versus (vs)-host disease Evidence of uncontrolled graft-versus-host disease Receiving systemic therapy for chronic graft-versus-host disease (topical therapy is allowed) Post allo patients must not have active graft versus-host disease and be off all immune suppression (other than steroids, as above) Any evidence of cGVHD or late acute graft versus host disease (aGVHD) between enrollment and first dose of obinutuzumab Active systemic treatment for graft versus host disease. HSCT recipients with active and/or chronic graft versus host disease Subject has received a prior HCT and has residual Chronic Graft-versus-host Disease (cGVHD) Hematopoietic stem cell transplantation (HSCT) within 60 days of screening, or receipt of immunosuppressive therapy for graft-versus-host disease treatment or prophylaxis within 14 days of first protocol therapy, or active graft-versus-host-disease Active graft-versus-host disease. Concomitant Medications\r\n* Corticosteroids: patients requiring corticosteroids who have not been on a stable or decreasing dose of corticosteroid for the 7 days prior to enrollment are not eligible; if used to modify immune adverse events related to prior therapy, >= 14 days must have elapsed since last dose of corticosteroid\r\n** Note: hydrocortisone used as a pre-medication to prevent transfusion related reactions is not considered a concomitant corticosteroid\r\n* Investigational drugs: patients who are currently receiving another investigational drug are not eligible\r\n* Anti-cancer agents: patients who are currently receiving other anti-cancer agents are not eligible (except patients receiving hydroxyurea, which may be continued until 24 hours prior to start of protocol therapy)\r\n* Anti-graft versus host disease (GVHD) or agents to prevent organ rejection post-transplant: patients who are receiving cyclosporine, tacrolimus or other agents to prevent either graft-versus-host disease post bone marrow transplant or organ rejection post-transplant are not eligible for this trial\r\n* Cardiac medications: any medications for treatment of left ventricular systolic dysfunction Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial Anti-GVHD agents post-transplant: Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial Patients who are receiving cyclosporine, tacrolimus or other agents to prevent either graft-versus-host disease post bone marrow transplant or organ rejection post-transplant are not eligible for this trial Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease (GVHD) post bone marrow transplant are not eligible for this trial Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial Participants who are receiving cyclosporine, tacrolimus or other agents to prevent GVHD post bone marrow transplant. Patients who are receiving cyclosporine, tacrolimus or other agents to prevent either graft-versus-host disease post bone marrow transplant or organ rejection post-transplant are not eligible for this trial Concomitant medications\r\n* Corticosteroids: patients receiving corticosteroids that have not been on a stable or decreasing dose for at least 7 days prior to enrollment are not eligible\r\n* Investigational drugs: patients cannot receive other investigational drugs while on this study\r\n* Anti-graft-versus-host disease (GVHD) drugs post-transplant: patients receiving cyclosporine, tacrolimus or other GVHD agents are not eligible Anti-graft-versus-host disease (GVHD) or agents to prevent organ rejection post-transplant: patients who are receiving cyclosporine, tacrolimus or other agents to prevent either graft-versus-host disease post bone marrow transplant or organ rejection post-transplant are not eligible for this trial Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial. Participants who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant Concomitant medications: \r\n* Investigational Drugs: Subjects who are currently receiving another investigational drug are not eligible \r\n* Anti-cancer Agents: Subjects who are currently receiving other anti-cancer agents are not eligible\r\n* Anti-graft-versus-host disease (GVHD) agents post-transplant: Subjects who are receiving cyclosporine, tacrolimus, or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial\r\n* Medications interfering with metabolism:\r\n** Medications which interfere with CYP3A4 and CYP2C8 metabolism, which metabolize nab-paclitaxel: subjects using these agents are not eligible for this trial; paclitaxel is metabolized by CYP3A4 and CYP2C8, so strong inhibitors or inducers of these enzymes should be avoided\r\n*** Note on use of trimethoprim/sulfamethoxazole: Trimethoprim/sulfamethoxazole should not be administered concomitantly with abraxane/gemcitabine, and patients must be monitored closely for toxicities Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial Anti-GVHD or agents to prevent organ rejection post-transplant; patients who are receiving cyclosporine, tacrolimus, or other agents to prevent either graft-versus-host disease post bone marrow transplant or organ rejection post-transplant are not eligible for this trial; at least 3 half-lives must have elapsed after the last dose of GVHD medications (meds) Concomitant medications \r\n* Corticosteroids: patients requiring corticosteroids who have not been on a stable or decreasing dose of corticosteroid for the 7 days prior to enrollment are not eligible\r\n* Patients who have received previous treatment with IMGN901 are not eligible\r\n* Investigational drugs: patients who are currently receiving another investigational drug are not eligible\r\n* Anti-cancer agents: patients who are currently receiving other anti-cancer agents are not eligible\r\n* Anti-graft-versus-host disease (GVHD) or agents to prevent organ rejection post-transplant: patients who are receiving cyclosporine, tacrolimus or other agents to prevent either graft-versus-host disease post bone marrow transplant or organ rejection post-transplant are not eligible for this trial Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial Anti-graft versus host disease (GVHD) agents post-transplant: \r\n* Patients who are receiving cyclosporine, tacrolimus or other agents to prevent graft-versus-host disease post bone marrow transplant are not eligible for this trial\r\n* Patients must be off all systemic immunosuppressive therapy for at least 2 weeks, excluding hydrocortisone for physiologic cortisol replacement Has undergone prior allogeneic hematopoietic stem cell transplantation within the last 5 years. (Note: Participants who have had a stem cell transplant >5 years ago are eligible as long as there are no symptoms of graft-versus-host disease [GVHD].) Has undergone solid organ transplant at any time, or prior allogeneic hematopoietic stem cell transplantation within the last 5 years. (Participants who have had an allogeneic hematopoietic transplant >5 years ago are eligible as long as there are no symptoms of Graft Versus Host Disease [GVHD].) Has undergone prior allogeneic hematopoietic stem cell transplantation within the last 5 years. (Subjects who have had a transplant greater than 5 years ago are eligible as long as there are no symptoms of graft versus host disease (GVHD). Has undergone prior allogeneic hematopoetic stem cell transplantation within the last 5 years. (Participants who have had a transplant greater than 5 years ago are eligible as long as there are no symptoms of Graft versus Host Disease [GVHD]). Has undergone prior allogeneic hematopoietic stem cell transplantation within the last 5 years. (Subjects who have had a transplant greater than 5 years ago are eligible as long as there are no symptoms of GVHD.) Patients who have undergone an allogeneic hematopoietic cell transplantation (HSCT) within the last 5 years (yrs) are eligible for enrollment if they have no signs or symptoms of active graft versus host disease (GvHD) and are off all immune suppressive medications Has undergone prior allogeneic hematopoietic stem cell transplantation within the last 5 years. Note: Participants who have had a transplant greater than 5 years ago are eligible as long as there are no symptoms of graft-versus-host disease (GVHD). No evidence of active graft versus host disease (GVHD) and >= 2 months must have elapsed since transplant or rescue Patients with graft versus-host disease (GVHD) Patients with evidence of graft versus host disease (GVHD) > grade II at time of enrollment Patients must have fully recovered from the acute effects of all prior therapy and cannot have evidence of graft-versus-host disease (GVHD) Evidence of graft versus host disease (GVHD) > grade II Evidence of graft versus host disease (GVHD) > grade II Evidence of graft versus host disease (GVHD) > grade II Grade III/IV acute graft-versus-host disease (GVHD) Presence of graft-versus-host disease (GVHD) more than grade 2 Presence of acute or chronic graft-versus-host disease (GVHD) unless limited to skin involvement and managed with topical steroid therapy alone Active acute graft versus host disease (GVHD) grade >= 2. Presence of acute or chronic graft-versus-host disease (GVHD) unless limited to skin involvement and managed with topical steroid therapy alone Active acute graft versus (vs.) host disease >= grade 2 or active extensive chronic graft versus host disease (GVHD) Presence of active acute or chronic graft versus host disease (GVHD) Graft versus host disease (GVHD) grade III or IV CRITERIA FOR LEUKAPHERESIS AND PRE-THERAPY EVALUATION: Presence of active acute or chronic graft versus host disease (GVHD) Patients with prior history of or active severe (grade 3 or 4) acute graft-versus-host disease (GVHD) Subjects must not have a history of severe (grade 3-4) acute graft versus host disease (GVHD), and/or current > grade 1 acute GHVD; subjects must not have a history of active chronic GVHD (whether limited or extensive stage) Active graft versus (vs.) host disease (gvhd) No uncontrolled graft versus host disease (GVHD) Active acute graft versus host disease (GVHD) grade II or higher Active acute or chronic graft-versus-host disease (GVHD) requiring systemic therapy Patients with active acute graft-versus-host disease (GVHD) grades II-IV Patients with active acute graft versus host disease (GVHD) grades II-IV. Patients with active acute graft-versus-host disease (GVHD) grades II-IV Patients with active acute graft-versus-host disease (GVHD) grades II-IV Active acute or chronic graft-versus-host disease (GVHD) Patients with untreated or uncontrolled grade 3 or 4 graft-versus-host disease (GVHD) Has active graft-versus-host disease (GVHD). Active graft-versus-host disease (GvHD) grades II-IV; prior acute GVHD could have occurred but resolved at time of initiation of daratumumab Acute graft versus host disease (GVHD) or active chronic GVHD greater than grade 1 Active acute graft-versus-host disease (GvHD) or chronic GVHD grade 2 or higher Presence of Grade 2 to 4 acute or extensive chronic graft-versus-host disease (GVHD) Presence of grade 2 to 4 acute or extensive chronic graft-versus-host disease (GVHD). Patient has evidence of graft versus host disease (GVHD) Patient has evidence of active graft versus host disease (GVHD) Anti Graft-Versus-Host Disease (GVHD) therapy within 12 weeks before the first dose of study drug Presence of acute or extensive chronic graft versus host disease (GVHD) Acute graft-versus-host disease (GvHD), classic (=< day 100) or late-onset (> day 100) Patients on investigational therapy for graft-versus-host disease (GVHD) Currently taking corticosteroids for therapy of graft-versus-host disease (GVHD) Presence of steroid-refractory acute graft-versus-host disease (GVHD) Less than 100 days post -transplant or any evidence of active graft-versus-host disease (GVHD) Acute graft-versus-host disease (GVHD) at time of enrollment (history of treated and resolved GVHD is permitted) Patients with active acute Graft versus host disease (GVHD) grades II-IV. Active acute graft-vs-host disease (GVHD) grades II-IV Active acute graft vs. host disease >= grade 2 or active extensive chronic graft-versus-host disease (GVHD) Patient has evidence of graft versus host disease (GVHD). Refractory graft versus host disease (GvHD) not responding to treatment Acute graft versus host disease (GVHD) fitting one of the following categories: Any graft-versus-host disease (GVHD) prophylaxis regimen is allowed Prior bone marrow transplant within 3 months or with acute graft versus host disease (GVHD) Patients actively enrolled on any other graft versus host disease (GVHD) prevention trial Patients with active acute graft-versus-host disease (GVHD) grades II-IV No signs or symptoms of acute graft versus host disease; however prior acute GVHD which is resolved and controlled with low dose steroids (< 0.3 mg/kg/day for at least 1 week) may be eligible Patients with graft-versus-host disease (GVHD) > grade II Presence of acute or chronic graft-versus-host disease (GVHD) Acute graft versus host disease (GvHD) Grade III or IV, or severe chronic GvHD. Patients are not eligible if they have had or are planned for solid organ transplant; patients who have received allogeneic hematopoietic stem cell transplant are eligible if:\r\n* The transplant occurred at least 90 days prior to registration, \r\n* Patient has no prior acute graft versus host disease (GVHD), and \r\n* Within 48 hours of registration, patient demonstrates at least 90% engraftment, defined as: absolute neutrophil count (ANC) >= 500 mcl, measured over 3 consecutive days or 1 day with an ANC >= 1,000 mcl, or platelets >= 50,000 mcl measured, wherein the patient did not receive any platelet transfusions within 7 days prior to laboratory assessment Patients may have received prior allogeneic transplant or autologous transplant; however, patients with prior allogeneic bone marrow transplant will be eligible only if both of the following conditions are met:\r\n* The transplant must have been performed >= 90 days prior to registration\r\n* The patient must not have >= grade 2 acute graft versus host disease (GvHD) or either moderate or severe limited chronic GvHD within 14 days prior to registration ELIGIBILITY CRITERIA - PHASE I (ARMS A, B, C): Patient may be enrolled with a prior allogeneic hematopoietic stem cell transplant (HSCT) but the transplant date must be at least 90 days before date of enrollment; patient must be off immunosuppression and without active graft versus host disease (GVHD) prior to enrollment if previous HSCT COHORT 1: Not be appropriate candidate for intensive salvage chemotherapy due to co-morbidities or other disease- or treatment-related factors\r\n* NOTE: Subjects who received prior treatment with hypomethylating agents either for myelodysplastic syndrome (MDS), myeloproliferative neoplasm (MPN), or AML will be eligible\r\n* NOTE: Subjects who had prior allogeneic stem cell transplant (alloHSCT) will be eligible as long as they have been at least 3 months after allogeneic HSCT and are off of all immune suppression for at least 3 weeks (>21 days) and have no evidence of active graft versus host disease (GVHD); subjects with prior alloHSCT will NOT be eligible for enrollment during the safety run in phase Stem cell infusion without TBI: no evidence of active graft versus host disease and at least 84 days must have elapsed after transplant, and 42 days for autologous stem cell infusion after I^131-MIBG therapy Autologous hematologic stem cell transplant within 3 months of study entry; allogeneic hematologic stem cell transplant within 6 months; grade II, or greater, active graft-versus-host disease No prior allogeneic transplant unless all of the following apply:\r\n* At least 5 years from time of transplant\r\n* Absence of clinically significant graft-versus-host disease (GVHD)\r\n* Not on immune suppression\r\n* Approval of overall PI Patients, who relapsed 6 months after bone marrow transplant and have no evidence of active graft versus host disease and are off systemic immunosuppressant medications for at least 2 months and have received hypomethylating agents (HMA) therapy before or after transplant and meet other eligibility criteria of progression after at least 4 months of DNMTi therapy, are eligible to be enrolled in this clinical trial Patients who have underwent autologous or allogeneic stem cell transplant =< 4 weeks prior to cycle 1 day 1 or have active graft-versus-host disease are excluded Receipt of an allogeneic transplant within 6 months or an autologous transplant within the preceding 3 months; evidence of ongoing graft-versus-host disease (GVHD) For subjects with prior allogeneic stem cell transplant, no evidence of active graft-versus host disease (GVHD), and must be >= 2 weeks off immunosuppressive therapy Prior allogeneic transplant performed ? 6 months prior to first dose of AMV564 is allowed provided there is no evidence of active graft-versus-host disease (GVHD) and the patient has been off immunosuppressive therapy for ? 4 weeks. If prior allogeneic stem cell transplant, history of moderate to severe chronic graft versus host disease (GVHD) Prior first allogeneic stem cell transplant, with any graft source, donor type, and GVHD prophylaxis Stem cell transplant recipients must have no evidence of active graft-versus-host disease Prior allogeneic stem cell transplant within 6 months of study drug administration and no requirement for graft versus host therapy. Cohort #2: patients with MCL with prior allogeneic hematopoietic stem cell transplant, minimum 6 months after transplant, not on immunosuppression, and without prior or active graft versus host disease (GVHD), are allowed Patients within 1 year of allogeneic stem cell transplant, patients with active graft versus host disease (GVHD) or requiring immunosuppression are excluded At least 9 months from stem cell transplant with no active graft versus host disease No evidence of active graft-versus-host disease (GVHD) and at least 100 days must have elapsed after allogeneic bone marrow transplant or stem cell infusion prior to study drug administration Has received a prior allogeneic hematopoietic stem cell transplant within the past 5 years, requires immunosuppression, or has evidence of active graft-versus-host-disease Patients with a prior allogeneic transplant ARE eligible UNLESS previously or currently experienced graft versus host disease (GvHD) that required systemic steroids or other systemic lymphotoxic therapy Received an allogeneic stem cell transplant in the past 1 year (if over 1 year post allogeneic transplant, must not have active chronic graft versus host disease [cGVHD]) Allogeneic stem cell transplant within the last 6 months, or active graft-versus-host disease following allogeneic transplant or autologous stem cell transplant within the last 3 months before the date of the first dose of study drug administration. Stem cell transplant recipients must have no evidence of and not receive treatment for graft-versus-host disease Patients with previous allogeneic stem cell transplant (SCT) if they meet either of the following criteria:\r\n* =< 60 days from allogeneic SCT \r\n* Active acute or chronic graft-versus-host-disease (GvHD) or receiving immunosuppressive therapy as treatment for GvHD Subjects are not a candidate, or have failed allogeneic stem cell transplantation. Subjects who underwent allo-transplant in the past are eligible under following conditions: transplant was >2 year prior to enrolment, and no evidence of active graft-versus-host disease (GVHD) Previous allogeneic bone marrow transplant are restricted, unless there is no evidence of acute or chronic graft versus host disease. Patients with previous allogeneic stem cell transplant (SCT) are excluded within 6 months or with active acute or chronic graft-versus host disease are excluded; patients must be off immunosuppression for graft versus host disease (GVHD) for at least 30 days before cycle 1 day Has had an allogeneic stem cell transplant with current active graft-versus-host-disease. Patients with relapsed disease after prior allogeneic SCT (myeloablative or nonmyeloablative) 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 Have undergone autologous or allogeneic stem cell transplant <60 days prior to receiving the first dose of ponatinib; have any evidence of ongoing graft-versus-host disease (GVHD) or GVHD requiring immunosuppressive therapy or are being considered for stem cell transplant within 6-12 months of enrollment (note: ponatinib is not to be used as a bridge to stem cell transplant in this trial) Patients with previous allogeneic stem cell transplant (SCT) within 6 months or with active acute or chronic graft-versus host disease are excluded; patients must be off immunosuppression for graft-versus host disease (GVHD) for at least 30 days before cycle 1 day 1 Patients having undergone prior allogeneic stem cell transplant within 3 months or having active graft versus host disease Patients with previous allogeneic stem cell transplant (SCT) if they meet either of the following criteria:\r\n* < 100 days from allogeneic SCT\r\n* Active acute or chronic graft-versus-host disease (GvHD), or\r\n* Receiving immunosuppressive therapy as treatment for GvHD within the last 7 days If patient has undergone prior allogeneic stem cell transplant, they must be greater than 100 days post transplant and have =< grade 2 graft-versus-host disease If a research participant has undergone prior allogeneic stem cell transplant, he/she must be off all immunosuppressants for graft versus host disease (GVHD) for at least 2 weeks before undergoing leukapheresis\r\n* Note: the above is not applicable if the research participant's done is undergoing leukapheresis If a research participant has undergone prior allogeneic stem cell transplant (alloSCT), and has documented =< grade 2 graft versus host disease (GVHD) but the donor is undergoing leukapheresis, the research participant may be considered eligible for enrollment (at the discretion of the study principal investigator [PI]) provided that immunosupressants can be tapered off completely prior to lymphodepletion Patients must have relapsed after first line chemotherapy; may have relapsed after autologous or allogeneic stem cell transplant, or have primary refractory disease; no upper limit for number of prior therapies; if status post allogeneic stem cell transplant, no active graft versus host disease Previous allogeneic stem cell transplant within 6 months prior to enrolment, active graft vs host disease (GVHD), or requiring transplant-related immunosuppression Patient had an allogeneic stem cell transplant within 6 months before first dose of PRLX 93936 or has evidence of graft versus host disease. Subjects after prior allogeneic SCT are allowed if the allogeneic transplant was performed >=2 years prior to study treatment, and if subject has no active Graft-versus- host disease (GVHD) requiring treatment, and meet the remaining eligibility criteria. Evidence of ongoing graft-versus-host disease (GvHD) if prior stem cell transplant (SCT). Prior allogeneic stem cell transplant with day 0 < 12 months prior and/or with chronic graft versus host disease (GVHD) requiring current use of immunosuppression; patients with prior allogeneic stem cell transplant with day 0 > 12 months prior who do not require immunosuppression for GVHD will be eligible Prior allogeneic stem cell transplant within 6 months of study drug administration and no requirement for graft versus host therapy. Stem cell transplant recipients must have no evidence of active graft-versus-host disease and should not be receiving treatment for it Allogeneic stem cell transplant less than 12 months prior to initiation of study treatment and who have not discontinued immunosuppressive treatment for at least four weeks prior to initiation of study treatment and who are currently dependent on such treatment; patients may also not have active graft versus (v.) host disease Prior hematopoietic stem cell transplant within 6 months of enrollment. If the subject had an allogenic transplant there must be no apparent signs of graft versus host disease and subjects must have discontinued all immunosuppressive therapies for at least 4 weeks Is within the first 100 days of having undergone an allogeneic stem cell transplant; otherwise, patients who have received an allogeneic stem cell transplant are allowed as long as they have no evidence of active graft versus host disease (GVHD) or are on immunosuppressive therapy At least one prior therapy for CLL/SLL; prior autologous or allogeneic stem cell transplant is allowed; patients may not be on chronic immunosuppressive therapy for graft-versus-host disease (GVHD); patients who are on only oral steroids must be on an oral dose of 10mg or less of prednisone (or equivalent) daily Unless approved by the medical monitor, may not have received an allogeneic hematopoietic stem cell transplant within 6 months before treatment, or have active graft-versus-host-disease following allogeneic transplant Prior allogeneic bone marrow progenitor cell transplant within 100 days or on active immunosuppression for graft versus host disease (GVHD) treatment or prophylaxis within 28 days prior to enrollment Allogeneic stem cell transplant within the last 6 months, or active-graft-versus-host disease following allogeneic transplant, or subjects currently on immunosuppressive therapy following allogeneic transplant Allogeneic stem cell transplant within the last 6 months, or active graft versus host disease following allogeneic transplant, or autologous stem cell transplant within the last 3 months. Post-autologous stem cell transplant (ASCT) or not a candidate for ASCT; prior allogeneic stem cell transplant is allowed if patient is off all immunosuppressives and has no evidence of active graft-versus-host disease (GVHD) If participant had prior allogeneic stem cell transplant (SCT), participant has evidence of ongoing graft-versus-host disease (GvHD). Subjects with a history of allogeneic stem cell transplant are eligible for study participation provided the following eligibility criteria are met: transplant was >60 days prior to study enrolment; subject has not taken immunosuppressive medications for at least 1 month; no signs or symptoms of graft versus host disease other than Grade 1 skin involvement; no active infection. Received allogeneic hematopoietic stem cell transplant within the last 6 months, or has active graft versus host disease (GVHD) following allogeneic transplant, or currently receiving immunosuppressive therapy following allogeneic transplant Allogeneic stem cell transplant within the previous 6 months, or active graft versus host disease following allogeneic transplant. Patients who have had allogeneic hematopoietic stem cell transplant (HSCT) are not eligible if they meet any of the following: \r\n* transplant is within 2 months from cycle 1, day 1 (C1D1) \r\n* Has clinically significant graft-versus-host disease requiring treatment\r\n* Has >= grade 3 persistent non-hematological toxicity related to the transplant Patients with previous allogeneic stem cell transplant (SCT) within 6 months or with active acute or chronic graft-versus host disease are excluded; patients must be off immunosuppression for GVHD for at least 60 days before cycle 1 day 1 Autologous hematologic stem cell transplant within 3 months of study entry; allogeneic hematologic stem cell transplant within 12 months; post allogeneic (allo) patients must not have active graft versus-host disease and be off all immune suppression (other than steroids, as above) Subjects can be enrolled and treated under this protocol regardless of their CLL treatment history or number of previous treatments; in addition, subjects with history of allogeneic stem cell transplant can be enrolled and treated unless they have active manifestations of graft versus (vs.) host disease (GVHD) or chronic illness or infections that will prevent them from completing the study Patients who have had a previous allogeneic transplant within 6 months and have evidence of clinically significant graft versus host disease Active graft-versus-host disease (GVHD) following allogeneic stem cell transplant for non-AML condition (ex. MDS, MPN, lymphoid malignancy, aplastic anemia) requiring ongoing use of immunosuppressants Patients within 1 year of allogeneic stem cell transplant, patients with active graft versus host disease (GVHD) or requiring immunosuppression are excluded Patients with relapsed disease after prior allogeneic SCT (myeloablative or nonmyeloablative) will be eligible if they meet all other inclusion criteria and:\r\n* 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-versus-host disease (GVHD) and require no immunosuppression\r\n* Are more than 6 months from transplant Patients who underwent stem cell transplant (SCT) in first complete remission are eligible, as long as all of the following criteria are met:\r\n* At least 100 days have elapsed since stem cell infusion\r\n* At least 14 days off of all medications for graft-versus-host-disease (GVHD) prophylaxis or treatment\r\n* No evidence of acute GVHD Patients who have undergone prior allogeneic transplant are excluded only if they remain on any immunosuppression or have signs or symptoms of clinical graft-versus-host disease Patients previously treated with allogeneic stem cell transplant (SCT) that is currently complicated by active graft versus host disease (GVHD) requiring T cell suppressive therapy Subjects who have undergone stem cell transplant who are undergoing treatment or prophylaxis for Graft versus host disease Patients who have experienced their relapse after a hematopoietic stem cell transplant (HSCT) are eligible, provided all of the following are met: \r\n* No evidence of acute or chronic graft-versus-host disease (GVHD)\r\n* At least 14 days off all medications for GVHD\r\n* At least 60 days post-transplant at the time of enrollment Hematopoietic Stem Cell Transplant: Patients who have experienced their relapse after a HSCT are eligible, provided they have no evidence of Graft-versus-Host Disease (GVHD) and are at least 60 days post-transplant at the time of enrollment. Hematopoietic Stem Cell Transplant: Patients who have had previous allogeneic HSCT must have grade I or less of Graft-versus-Host Disease (GVHD) and have not received immunosuppressive medication for at least 90 days. Patients with previous allogeneic stem cell transplant (SCT) if they meet either of the following criteria: < 100 days from allogeneic SCT, acute or chronic graft-versus-host disease (GvHD), or receiving immunosuppressive therapy as treatment for or prophylaxis against GvHD within the last 7 days Autologous or allogeneic stem cell transplant within 3 months prior to enrolment [NOTE: subjects with evidence of active graph versus host disease are excluded]. Participants who are less than 100 days post-transplant, or greater than or equal to 100 days post-transplant with active graft versus host disease (GVHD), or are receiving immunosuppressant therapy within 7 days prior to first dose of study drug. Prior allogeneic stem cell transplant patients will be allowed to enroll if they are past day +100 of transplant, have no active graft-versus-host-disease, are not on any immunosuppressants and have been off immunosuppressants for at least 4 weeks; prior autologous stem cell transplant patients will also be allowed to enter this study if they are past their day +100 of transplant Patients must have recovered from the acute side effects of all prior anticancer therapy\r\n* At least 1 week from prior cytotoxic chemotherapy\r\n* At least 4 weeks from craniospinal irradiation\r\n* At least 4 months since hematopoietic stem cell transplant (HSCT) with no evidence of active graft-versus-host disease (GVHD) Subject may not have had hematopoietic stem cell transplant (HSCT) meeting any of the following: \r\n* Is within 2 months of transplant from cycle 1 day 1 (C1D1) \r\n* Has clinically significant graft-versus-host disease requiring treatment\r\n* Has >= grade 2 persistent non-hematological toxicity related to the transplant \r\n* Donor lymphocyte infusion (DLI) is not permitted < 30 days prior to study registration Patients with previous allogeneic stem cell transplant (SCT) within 6 months or with active acute or chronic graft-versus host disease are excluded; patients must be off immunosuppression for graft-versus host disease (GVHD) for at least 30 days before cycle 1 day 1 Hematopoietic stem cell transplant recipients with chronic thrombocytopenia due to chronic graft-versus-host disease (GVHD) or other causes Phase II: Received an autologous or allogeneic stem cell transplant at the Hospital of the University of Pennsylvania and experienced a sentinel event of either 1) disease relapse, 2) severe (grade III or IV) graft-versus-host disease, or 3) unplanned hospital admission with length of stay greater than 72 hours Previous allogeneic hematopoietic stem cell transplant within 6 months prior to enrollment, active graft versus host disease (GVHD), or requiring transplant-related immunosuppression. Prior allogeneic stem cell transplant with active graft-versus-host- disease (GVHD). Previously received an allogeneic stem cell transplant and the occurrence of one or more of the following: received the transplant within 6 months prior to study day 1;received immunosuppressive therapy within the last 3 months prior to study day 1;having signs or symptoms of acute or chronic graft-versus-host disease. Prior allogeneic stem cell transplant, no evidence of active graft-versus host disease (GVHD) and must be ? 2 weeks off immunosuppressive therapy.