Prior allogeneic stem cell transplant Patients who have received prior allogeneic stem cell transplant B-cell lymphoma patients who have received prior allogeneic stem cell transplant Allogeneic stem cell transplant within 100 days before first dose of study drug Patients must not have received allogeneic stem cell transplant Previous allogeneic stem cell transplant Undergone an allogeneic stem cell transplant within the past 1 year Prior allogeneic stem cell transplant. Prior allogeneic stem cell transplant Previous allogeneic stem cell transplant Less than 30 days post-allogeneic stem cell transplant Less than 30 days post-allogeneic stem cell transplant Prior allogeneic stem cell transplant with either standard or reduced intensity conditioning ? 6 months prior to starting CC-90002. Patients must have received an allogeneic stem cell transplant for a hematologic malignancy Has received an allogeneic stem cell transplant Allogeneic stem cell transplant within the past 1 year History of allogeneic stem cell transplant. One prior allogeneic stem cell transplant within the preceding 24 months. Patients who have received prior allogeneic stem cell transplant will be permitted to enroll on the protocol Prior allogeneic stem cell transplant is not permitted History of allogeneic stem cell transplant Relapsed or refractory disease after allogeneic transplant provided subject is at least 100 days from stem cell transplant at the time of enrollment Prior allogeneic stem cell transplant or organ graft Prior stem cell transplant. History of stem cell transplant. Prior allogeneic stem cell transplant Prior stem cell transplant Prior allogeneic stem cell transplant is not permitted Allogeneic hematologic stem cell transplant within 12 months of study entry Prior allogeneic stem cell transplant Eligible and willing to proceed with an allogeneic stem cell transplant with an acceptable stem cell donor Prior allogeneic stem cell transplant Patients with the diagnosis of severe AA, who are not currently candidates for an allogeneic stem cell transplant, fulfilling the following criteria: Patients had prior autologous or allogeneic stem cell transplant; prior stem cell collection is allowed Diagnosis of a hematological malignancy requiring an allogeneic stem cell transplant consistent with the standard of care Patient with MDS who relapse after allogeneic stem cell transplant are eligible if they received standard dose decitabine or 5-azacytidine prior to or after stem cell transplant Patients with the diagnosis of aplastic anemia who are either previously treated or untreated are eligible if they are not currently candidates for an allogeneic stem cell transplant Patients that are eligible (including having available donor) and willing to receive an allogeneic stem cell transplant within 4 weeks One prior allogeneic stem cell transplant within the preceding 24 months Prior allogeneic stem cell transplant. Previously received allogeneic stem cell transplant and one or more of the following: Patients who have received prior allogeneic stem cell transplant Patients status post-allogeneic stem cell transplant are not eligible History of allogeneic organ or stem cell transplant Allogeneic organ or stem cell transplant Ineligible for allogeneic stem cell transplant All patients with relapsed/refractory lymphoma must have received or be ineligible for autologous stem cell transplant or be ineligible for allogeneic stem cell transplant\r\n* NOTE: Patients must not have had a prior allogeneic stem cell transplant Patients are not eligible who have had a prior allogeneic stem cell transplant\r\n* NOTE: Autologous stem cell transplant is acceptable Patients with a history of allogeneic stem cell transplant for MDS or any other antecedent hematologic disorder are not eligible Prior allogeneic stem cell transplant They have had an allogeneic stem cell transplant (received stem cell from someone else) Patients status post allogeneic stem cell transplant. Previous allogeneic stem cell transplant. Patients may have had a prior autologous stem cell transplant; no prior history of allogeneic stem cell transplant Prior allogeneic stem cell transplant Participants received an allogeneic stem cell transplant Relapsed or refractory disease after allogeneic transplant provided subject is at least 100 days from stem cell transplant at the time of enrollment Prior allogeneic stem cell transplant Patients undergoing allogeneic stem cell transplant using a peripheral blood stem cell source Previously received an organ or allogeneic progenitor/stem cell transplant. Subject has undergone an allogeneic stem cell transplant within the past year Prior allogeneic stem cell transplant Patient must not have undergone a prior allogeneic stem cell transplant One prior allogeneic stem cell transplant within the preceding 24 months Patients who can receive an allogeneic stem cell transplant within 4 weeks. Prior allogeneic stem cell transplant A prior allogeneic stem cell transplant CLL subject has undergone an allogeneic or autologous stem cell transplant or NHL subject has undergone an allogeneic stem cell transplant or has been diagnosed with Post-Transplant Lymphoproliferative Disease, Burkitt's lymphoma, Burkitt-like lymphoma, or lymphoblastic lymphoma/leukemia. Had allogeneic stem cell transplant within last 6 months and on immunosuppressive therapy. Previous allogeneic stem cell transplant Prior allogeneic stem cell transplant Stem cell transplant within 60 days Previous allogeneic stem cell transplant Patients who are candidates for allogeneic stem cell transplant at the time of enrollment Patients status post-allogeneic stem cell transplant are not eligible. Candidates for allogeneic stem cell transplant at the time of screening. For Pre-allo Part A (before stem cell transplant): Eligible for an allogeneic hematopoietic stem cell transplant Prior stem cell transplant Current candidacy for a potentially curative allogeneic stem cell transplant, unless declined Patients who are eligible, willing and able to receive an allogeneic stem cell transplant within 6 weeks are not eligible Prior allogeneic stem cell transplant in previous 3 months History of (or plans to undergo) spleen removal surgery or allogeneic stem cell transplant History of allogeneic stem cell transplant Prior allogeneic stem cell transplant Prior allogeneic stem cell transplant Patients <100 days since prior allogeneic stem cell transplant Patients with previous allogeneic stem cell transplant. Participants with a history of allogeneic stem cell transplant are eligible for study participation provided the following eligibility criteria are met: AML patients who are candidates for allogeneic stem cell transplant are excluded. Prior allogeneic stem cell transplant, except for a specific cohort Patients who have received a prior allogeneic stem cell transplant are eligible if: Prior organ or allogeneic stem cell transplant Subject has undergone an allogeneic stem cell transplant Allogeneic stem cell transplant (SCT) Need for cytoreduction prior to allogeneic stem cell transplant. Patients are not eligible post allogeneic stem cell transplant. The patient is not considered to be an immediate candidate for allogeneic stem cell transplant as determined by the investigator. History of allogeneic stem cell transplant Received an allogeneic stem cell transplant <3 months prior to the first dose of study medication, or presence of polymerase chain reaction (PCR)-detectable cytomegalovirus (CMV) in any post-allogeneic transplant participant Prior allogeneic stem cell transplant. Prior stem cell transplant Prior allogeneic stem cell transplant more than 6 months from the first transplant, in remission History of allogeneic stem cell transplant or transplant eligible Patients who have had an allogeneic stem cell transplant are excluded Planned allogeneic stem cell transplant with schedule that accommodates at least a 5 week exercise intervention, but not greater than 12 weeks ELIGIBILITY FOR CD34 SELECTED STEM CELL INFUSION FOLLOWING PRIOR ALLOGENEIC STEM CELL TRANSPLANT (MAY BE REFERRED TO AS A \BOOST\) Prior allogeneic stem cell transplant Prior allogeneic stem cell transplant with either standard or reduced intensity conditioning. DONOR: Donors undergoing stem cell collection for match related allogeneic stem cell transplant Subjects planning to undergo allogeneic stem cell transplant within 6 months of enrollment Prior allogeneic stem cell transplant and/or chimeric antigen receptor T-cell therapy at any time. Have received allogeneic stem cell transplant.