Presence of central nervous system (CNS) involvement requiring active treatment Leukemia with active central nervous system (CNS) involvement Active central nervous system (CNS) involvement by leukemia Known active central nervous system (CNS) involvement by lymphoma, including parenchymal and/or lymphomatous meningitis Active, uncontrolled central nervous system (CNS) involvement by lymphoma Patients with known active central nervous system (CNS) involvement by lymphoma, including leptomeningeal involvement Known active central nervous system (CNS) involvement by lymphoma should be excluded from this clinical trial Active central nervous system (CNS) involvement with leukemia Active, uncontrolled central nervous system (CNS) leukemia involvement Subject has known active central nervous system (CNS) involvement from AML Active central nervous system (CNS) involvement by lymphoma, including untreated symptomatic epidural disease Patients with active central nervous system (CNS) involvement with lymphoma are not eligible Participant has known active central nervous system (CNS) involvement with AML. Patients with known active central nervous system (CNS) disease, including leptomeningeal involvement Active central nervous system (CNS) involvement by malignancy Active central nervous system (CNS) metastases and/or leptomeningeal involvement Known active central nervous system (CNS) involvement Known active central nervous system (CNS) involvement by MM Subject has known active central nervous system (CNS) involvement with AML Evidence of active central nervous system (CNS) involvement known active central nervous system (CNS) involvement by malignancy. Active central nervous system (CNS) or testicular involvement by leukemia No active central nervous system (CNS) metastatic disease. NOTE: Subjects with CNS involvement must meet ALL of the following to be eligible: History of or known active central nervous system (CNS) involvement with AML Active central nervous system (CNS) involvement or leptomeningeal involvement Patients with known active central nervous system (CNS) disease, including leptomeningeal involvement Active, untreated central nervous system (CNS) involvement Active central nervous system (CNS)-only involvement by malignancy (note: participants with secondary CNS involvement are allowed on study) Patients with active central nervous system (CNS) involvement with lymphoma are not eligible History of or active central nervous system (CNS) or peripheral nerve stimulation (PNS) involvement Has known clinically active central nervous system (CNS) involvement Active central nervous system (CNS) involvement within the previous 2 months Active central nervous system (CNS) involvement of the underlying malignancy Active central nervous system (CNS) neoplastic involvement Known active central nervous system (CNS) involvement Patient with active central nervous system (CNS) involvement Patients with active central nervous system (CNS) involvement by malignant cells History of or known active central nervous system (CNS) involvement or leptomeningeal involvement Active central nervous system (CNS) involvement or leptomeningeal metastases involvement Known active central nervous system (CNS) involvement with AML at study entry Has known clinically active central nervous system (CNS) involvement OR history of resolved CNS involvement by multiple myeloma Patients with history of central nervous system (CNS) involvement or active CNS involvement by malignancy Active central nervous system (CNS) involvement by malignancy Active Central Nervous System (CNS) involvement by malignancy Has known clinically active central nervous system (CNS) involvement Have active leukemic involvement of the central nervous system (CNS). Active central nervous system (CNS) involvement of disease Active AML involvement of the central nervous system (CNS) with disease refractory to intrathecal chemotherapy AML patients with known, active leptomeningeal/central nervous system (CNS) involvement No active extramedullary leukemia or known active central nervous system (CNS) involvement by malignancy; such disease treated into remission is permitted Active central nervous system (CNS) involvement with leukemia Participant has known active central nervous system (CNS) involvement with AML. Any past or current Central Nervous System (CNS) involvement, including leptomeningeal leukemia. Patients with active central nervous system (CNS) involvement with lymphoma should be excluded from this clinical trial Patient with active central nervous system (CNS) involvement with lymphoid malignancy Active diagnosis of central nervous system (CNS) involvement with CLL Active central nervous system (CNS) disease involvement Clinically active central nervous system (CNS) cancer involvement. Imaging to exclude CNS involvement not required. Known active cerebral/meningeal involvement with lymphoma; asymptomatic patients with previously treated and resolved central nervous system (CNS) lymphoma involvement are permitted Had evidence of active central nervous system (CNS) involvement Active central nervous system (CNS) lymphoma/leukemia - Patients with prior CNS involvement are eligible provided that it has been treated and is in remission Active or symptomatic central nervous system (CNS) disease or epidural involvement Active involvement of the Central Nervous System (CNS). Active central nervous system (CNS) involvement of their malignancy. No active extramedullary leukemia or known active central nervous system (CNS) involvement by malignancy; such disease treated into remission is permitted Active central nervous system (CNS) involvement by malignancy No active extramedullary leukemia or known active central nervous system (CNS) involvement by malignancy; such disease treated into remission is permitted Patient must not have active central nervous system (CNS) involvement Active central nervous system (CNS) involvement by malignant cells EXCLUSION CRITERIA FOR ENROLLMENT (PRE-TRANSPLANT): Active involvement of the central nervous system with malignancy (previous central nervous system [CNS] involvement is allowed if clearance of CNS disease has been documented prior to enrollment) Active central nervous system (CNS) involvement by malignant cells Active central nervous system (CNS) involvement by malignant cells Active central nervous system (CNS) involvement by malignant cells Clinical suspicion of active central nervous system (CNS) involvement by leukemia