Known central nervous system involvement by PTCL Patients with evidence of current central nervous system leukemic involvement Central nervous system involvement Presence of active/uncontrolled central nervous system involvement Patients with any central nervous system involvement or CTCL. Central nervous system involvement Central nervous system involvement by lymphoma, including leptomeningeal involvement EXCLUSION - INFUSION: Patients with central nervous system involvement Myeloma-related central nervous system involvement Central nervous system involvement Central nervous system involvement with lymphoma at any time in the patient’s history; intrathecal prophylaxis during induction is allowed as long as active disease has not been identified Suggestive central nervous system involvement with leukemia Central nervous system involvement Symptomatic central nervous system involvement. Central nervous system involvement. Known central nervous system or meningeal involvement (in the absence of symptoms investigation into central nervous system involvement is not required) Evidence of lymphoma outside of the central nervous system\r\n* Ocular involvement will not exclude Known central nervous system involvement Known active involvement of the central nervous system by lymphoma or leukemia Subjects are not eligible if there is a prior history or current evidence of central nervous system or leptomeningeal involvement Has either clinical evidence of or history of central nervous system involvement by AML. Active or previous central nervous system leukemia involvement Patients who have known central nervous system involvement with multiple myeloma will be excluded from this clinical trial Active or previous central nervous system leukemia involvement Central nervous system involvement with MM (by clinical symptoms and signs). Active involvement of the central nervous system with malignancy No known history or suspicion of central nervous system involvement by lymphoma Central nervous system metastases, including leptomeningeal involvement Known central nervous system involvement with the disease under study Primary central nervous system involvement only Patients with known central nervous system involvement should be excluded from this clinical trial Has known active central nervous system involvement of the malignancy. Patients with known or suspected central nervous system involvement of lymphoma. All patients with central nervous system involvement with lymphoma Known lymphomatous involvement of the central nervous system History of central nervous system multiple myeloma involvement Subjects with known central nervous system involvement with multiple myeloma Active involvement of the central nervous system with malignancy Known active central nervous system involvement Central nervous system involvement of the disease under study Central nervous system involvement Known lymphomatous involvement of the central nervous system Known central nervous system involvement Presence of central nervous system involvement of leukemia or a history of primary central nervous system leukemia. Patients must not have active central nervous system involvement Primary central nervous system lymphoma or known intracranial involvement Subjects are not eligible if there is a prior history or current evidence of central nervous system or leptomeningeal involvement Known central nervous system or meningeal involvement (in the absence of symptoms, investigation into central nervous system involvement is not required) Active involvement of the central nervous system with malignancy Active involvement of the central nervous system with malignancy Central nervous system involvement. Active central nervous system involvement with AML. Known central nervous system or meningeal involvement (in the absence of symptoms, investigation into central nervous system involvement is not required) Known active involvement of the central nervous system by lymphoma or leukemia Known central nervous system involvement by multiple myeloma Patients with known central nervous system involvement should be excluded from this clinical trial Central nervous system involvement (Bing-Neel syndrome) Known involvement of central nervous system Central nervous system involvement by lymphoma, including leptomeningeal involvement Clinical evidence of central nervous system involvement. Known central nervous system involvement or brain metastases Active central nervous system involvement by leukemia Active central nervous system involvement Patients with a history of central nervous system involvement by CLL or who have prolymphocytic leukemia (PLL) Patients with documented central nervous system involvement of AML Active central nervous system involvement by malignancy Documented current central nervous system involvement by multiple myeloma History of or current, central nervous system involvement with AML. Known clinically active central nervous system involvement. Subject has known active central nervous system involvement with AML. Patients with controlled asymptomatic central nervous system involvement are allowed. Central nervous system involvement with lymphoma, including parenchymal and leptomeningeal disease Subjects with Central Nervous System involvement with multiple myeloma Central nervous system involvement of the CLL Active uncontrolled central nervous system involvement Presence or history of central nervous system involvement by lymphoma. Patients with known central nervous system involvement at the time of study entry will be excluded from this clinical trial Primary or secondary Central Nervous System involvement by lymphoma. Myeloma-related central nervous system involvement Patients with leukemic involvement of the central nervous system Central nervous system involvement (based on clinical assessment) Known clinically active central nervous system involvement Known active involvement of the central nervous system by lymphoma or leukemia Central nervous system involvement Known lymphomatous involvement of the central nervous system. Known central nervous system or meningeal involvement (in the absence of symptoms investigation into central nervous system involvement is not required) Active central nervous system involvement by lymphoma Known central nervous system involvement Central nervous system involvement. Known involvement of the central nervous system by WM. Central nervous system involvement Patients with a history of central nervous system involvement by lymphoma Active involvement of the central nervous system with malignancy Central nervous system disease involvement Central nervous system involvement Known Central nervous system involvement, brain metastasis Known central nervous system or meningeal involvement (in the absence of symptoms investigation into central nervous system involvement is not required); patients with human T-cell lymphotropic virus type 1 (HTLV1) adult T-cell leukemia/lymphoma (ATLL) and controlled central nervous system (CNS) or meningeal involvement may be enrolled after discussion with the Memorial Sloan Kettering (MSK) principal investigator Known active central nervous system involvement Central nervous system involvement. Presence or history of central nervous system involvement by lymphoma Known central nervous system involvement by leukemia No known central nervous system involvement by myeloma. Disease-related central nervous system involvement Documented current central nervous system involvement by leukemia or lymphoma CLL central nervous system involvement No known involvement of central nervous system by lymphoma Evidence of sanctuary site involvement by disease, e.g., central nervous system, ocular, testicular involvement Active involvement of the central nervous system with malignancy Untreated central nervous system involvement Known central nervous system involvement Known central nervous system involvement Active central nervous system involvement by malignancy; central nervous system disease that has been treated into remission is permitted; a chart note of the clinician’s impression of lack of central nervous system (CNS) involvement is acceptable Documented current central nervous system involvement Symptomatic central nervous system involvement Known uncontrolled central nervous system involvement Lymphoma involvement of the central nervous system For Part B only: Known leukemic involvement or clinical symptoms of leukemic involvement of the central nervous system Central nervous system involvement Patients with a history of central nervous system involvement by lymphoma Patients with known central nervous system involvement. Known, active (symptomatic) involvement of the central nervous system by leukemia. Known leukemic involvement of the central nervous system. Documented current central nervous system involvement by leukemia or lymphoma Central nervous system involvement Has central nervous system involvement History of central nervous system involvement of lymphoma; All patients with active central nervous system involvement with lymphoma INCLUSION CRITERIA FOR PATIENTS: No central nervous system involvement of disease Patients with active central nervous system involvement Symptomatic central nervous system involvement. History of central nervous system involvement or symptoms suggestive of central nervous system involvement by multiple myeloma Known central nervous system involvement by multiple myeloma Known uncontrolled central nervous system involvement by malignant disease