Central nervous system (CNS) involvement; CNS status must be confirmed by lumbar puncture\r\n* Note: lumbar puncture can be performed at the time of diagnosis and does not need to be repeated unless there is a change in neurological status or it was performed more than days prior to study entry NOTE: A lumbar puncture is not required in order to be enrolled on study nor are lumbar punctures recommended at the time of diagnosis; if the diagnosis of APL is known or suspected, diagnostic lumbar punctures in patients with neurologic symptoms should be deferred until any coagulopathy is corrected; if central nervous system (CNS) disease is suspected or proven, a computed tomography (CT) or magnetic resonance imaging (MRI) should be considered to rule out the possibility of an associated chloroma; if CNS disease is documented, patients are still eligible and will receive protocol directed intrathecal treatments Patients must have a lumbar puncture to determine CNS involvement of ALL within days prior to registration; patients with CNS are excluded from the trial; patients with CNS or CNS will be eligible, but will be monitored for CNS involvement; note that intrathecal methotrexate administered during the pre-study lumbar puncture may count as the first dose of intrathecal therapy required as part of the study Current clinical central nervous system (CNS) symptoms deemed by the investigator to be related to leukemic CNS involvement (no lumbar puncture required, clinical assessment per investigators judgment is sufficient) Patients must not have active central nervous system (CNS) involvement (by clinical evaluation); patients with previous documented history of CNS involvement of acute leukemia, or with clinical signs or symptoms consistent with CNS involvement of acute leukemia, must have a lumbar puncture which is negative for CNS involvement of acute leukemia; the lumbar puncture must be completed within days prior to registration; patients with no previous history of documented CNS involvement and with no clinical signs or symptoms consistent with CNS involvement are not required to have completed a lumbar puncture before registration; note that treatment with intrathecal therapy is recommended during protocol treatment but CNS analysis during treatment is not required Participants must have a lumbar puncture with negative cerebral spinal fluid cytology within weeks prior to enrollment Mantle cell NHL: may be treated in first complete remission (CR); (diagnostic lumbar puncture [LP] required pre-transplant) Active involvement of the central nervous system (CNS) by lymphoma; work-up for CNS involvement at diagnosis will be directed as per the treating physician and will depend on specific clinical circumstances (no brain imaging or lumbar puncture is required by this protocol) Clinical evidence suggestive of central nervous system (CNS) involvement with MDS unless a lumbar puncture confirms the absence of leukemic blasts in the cerebrospinal fluid (CSF) Brain metastases with risk of mass effect that would contraindicate lumbar puncture Active central nervous system (CNS) involvement of leukemia (lumbar puncture not required to rule out CNS involvement if not suspected) Mantle cell NHL-may be treated in first complete remission (CR); (diagnostic lumbar puncture [LP] required pre-transplant) Prior or active central nervous system (CNS) involvement by myeloma (eg leptomeningeal disease); screening for this, for example, by lumbar puncture, is only required if suspicious symptoms or radiographic findings are present Absence of active central nervous system (CNS) involvement; NOTE: pre-enrollment lumbar puncture not mandatory Known cytopathologically confirmed central nervous system (CNS) infiltration (in absence of suspicion of CNS involvement, lumbar puncture not required) Subjects who within days prior to randomization have had major surgery or a lumbar puncture (or epidural steroid injection); Have prior or active central nervous system (CNS) involvement (e.g. leptomeningeal disease, parenchymal masses) with myeloma; screening for this (e.g. with lumbar puncture) is not required unless suspicious symptoms are present Patients with clinical contraindication against lumbar puncture or Ommaya placement are NOT eligible for either Stratum Clinical evidence of (parenchymal or meningeal) central nervous system (CNS) involvement or metastasis; in subjects suspected of having CNS disease, a magnetic resonance imaging (MRI) scan of the brain and lumbar puncture should be done to confirm Active central nervous system (CNS) lymphoma within two weeks of registration; patients with a history of CNS involvement must have adequate treatment as defined by at least two negative spinal fluid assessments separated by at least one week; (otherwise lumbar puncture [LP] is not required if no clinical suspicion or evidence of CNS involvement); patients who have received cranial radiation therapy must still be eligible to receive total lymphoid irradiation to Gy Suspected AML-related central nervous system involvement; a lumbar puncture (LP) is not required to exclude central nervous system (CNS) disease Subjects must not have prior or active central nervous system (CNS) involvement (e.g. leptomeningeal disease, parenchymal masses) with myeloma; screening for this (e.g. with lumbar puncture) is not required unless suspicious symptoms are present Active central nervous system (CNS) disease defined as symptomatic meningeal lymphoma or known CNS parenchymal lymphoma; a lumbar puncture demonstrating DLBCL at the time of registration to this study is not exclusion for study enrollment Known central nervous system (CNS) lymphoma or leukemia; subjects with symptoms of CNS disease must have a negative computed tomography (CT) scan or negative diagnostic lumbar puncture prior to first dose Central nervous system (CNS) leukemic involvement not clearing with intrathecal chemotherapy; diagnostic lumbar puncture is to be performed Known cytopathologically confirmed CNS infiltration (in absence of suspicion of CNS involvement, lumbar puncture not required) Patients with suspected central nervous system (CNS) involvement should undergo lumbar puncture; those with documented CNS involvement will be excluded Central nervous system involvement; a lumbar puncture does not need to be performed unless there is clinical suspicion of leptomeningeal disease Patients with suspected or proven central nervous system (CNS) leukemia; (diagnostic lumbar puncture not required before enrollment) History of known leptomeningeal involvement (lumbar puncture not required) Patients must not have active involvement of the central nervous system (CNS) with MM (by clinical evaluation); patients with documentation of, or clinical signs or symptoms consistent with, CNS involvement of MM must have a lumbar puncture that is negative for CNS involvement of MM; the lumbar puncture must be completed within days prior to registration; patients with no previous history of documented CNS involvement and with no clinical signs or symptoms consistent with CNS involvement are not required to have completed a lumbar puncture prior to registration; note that monitoring of CNS involvement and treatment with intrathecal therapy is recommended during protocol treatment Patients must be able to tolerate lumbar puncture and/or Ommaya taps Known central nervous system lymphoma or leukemia; subjects with symptoms of CNS disease must have a negative CT scan or negative diagnostic lumbar puncture prior to randomization Current clinical central nervous system (CNS) symptoms deemed by the investigator to be related to leukaemic CNS involvement (no lumbar puncture required, clinical assessment per investigators judgement is sufficient). Central nervous system (CNS) leukemic involvement not clearing with intrathecal chemotherapy and/or cranial radiation prior to initiation of conditioning; diagnostic lumbar puncture is to be performed per protocol Known cytopathologically confirmed central nervous system (CNS) infiltration (in absence of suspicion of CNS involvement, lumbar puncture not required) Central nervous system involvement as documented by spinal fluid cytology or imaging. Subjects who have signs or symptoms suggestive of leukemic meningitis or a history of leukemic meningitis must have a lumbar puncture procedure performed within two weeks prior to randomization. Known Central Nervous System (CNS) lymphoma; subjects with symptoms of CNS disease must have a negative CT scan and negative diagnostic lumbar puncture Known active and uncontrolled central nervous system (CNS) involvement of leukemia (a lumbar puncture does not need to be performed as a part of screening) Known central nervous system (CNS) leukemia by spinal fluid cytology, flow cytometry or imaging; a lumbar puncture is not required unless CNS involvement is clinically suspected; patients with signs or symptoms of leukemic meningitis must have a negative lumbar puncture within weeks of study enrollment No history of lumbar surgery or other pre-existing spinal conditions that would preclude frequent, safe, reliable lumbar punctures Patients with known central nervous system (CNS) leukemia by spinal fluid cytology, flow cytometry or imaging; a lumbar puncture is not required unless CNS involvement is clinically suspected; patients with signs or symptoms of leukemic meningitis or a history of leukemic meningitis must have a negative lumbar puncture within weeks of study enrollment Recipient must have adequate neurologic function as defined by NO evidence of a severe central or peripheral neurologic abnormality. Patients with a history of previous CNS tumor involvement are eligible provided they are without symptoms or signs and the CNS is now free of disease on lumbar puncture and CT scan of the brain. Pediatric oncology patients undergoing a lumbar puncture in the Pediatric Sedation Suite; patients may or may not be receiving intrathecal chemotherapy Active CNS leukemia. Patients with symptoms of CNS involvement, particularly those with M or M subtypes, should undergo lumbar puncture prior to treatment on study to exclude CNS disease. Symptoms include cranial neuropathies, other neurologic deficits, and headache. Patients must be able to tolerate lumbar puncture and/or Ommaya taps Mantle-cell NHL - may be treated in first complete remission (CR); (diagnostic lumbar puncture [LP] required pre-transplant)