Central nervous system disease Patients must not be known to have AML in the central nervous system (CNS) Central nervous system (CNS) status must be determined based on a sample obtained prior to the administration of any systemic or intrathecal chemotherapy, with the exception of steroid pretreatment Patients with central nervous system (CNS) disease are not eligible AML patients with active central nervous system (CNS) disease will be excluded. Active extramedullary AML in testes or central nervous system (CNS) Non-central nervous system (CNS) radiotherapy within 1 week prior to C1D1 of study therapy History or evidence of uncontrollable central nervous system (CNS) disease Participant must not have a known uncontrolled malignancy of the central nervous system. Subject has known current central nervous system (CNS) disease Presence of any active central nervous system (CNS) disease at the time of evaluation (parenchymal or leptomeningeal) Known central nervous system mass lesion Patients with central nervous system involvement by ALL are eligible and may receive concomitant treatment with radiation therapy and/or intrathecal chemotherapy in accordance with standard medical practice; for patients with central nervous system (CNS) disease, dexamethasone may be temporarily administered instead of prednisone to reduce CNS pressure, at the discretion of the treating physician and after discussion with the Memorial Sloan-Kettering (MSK) principal investigator (PI); once dexamethasone is no longer needed, prednisone should be given as per protocol for 28 days Has a history of primary central nervous system malignancy. History of central nervous system (CNS) disease is acceptable if effectively treated and demonstrated stable disease for >= 2 months from protocol tissue procurement Active central nervous system (CNS) disease at time of screening. Participants must be >= 2 weeks since any prior radiation, including central nervous system (CNS) radiation Patients with primary central nervous system (CNS) cancer. Participants must be >= 2 weeks since any prior radiation, including central nervous system (CNS) radiation Active central nervous system (CNS) disease. Central nervous system malignancy Measurable disease according to RECIST v1.1 (must be outside central nervous system (CNS)) Central nervous system (CNS) tumors Central nervous system (CNS) disease Active extramedullary AML in testes or central nervous system (CNS) Patients with retinoblastoma protein (Rb1) positive recurrent, progressive or refractory central nervous system (CNS) tumors Uncontrolled metastatic disease to the brain or central nervous system (CNS). Without clinical signs of active central nervous system disease Presence of central nervous system (CNS) disease, which is symptomatic TREATMENT WITH SJCAR19: Central nervous system (CNS)-3 disease with or without neurologic changes Patients must not have evidence of active central nervous system (CNS) disease Evidence of > grade 1 central nervous system (CNS) hemorrhage on the baseline MRI scan. Recurrent or refractory ALL limited to isolated testicular or isolated central nervous system (CNS) disease Primary central nervous system malignancy Active central nervous system (CNS) or extramedullary disease Known central nervous system malignancy. Note: Central nervous system imaging is only required in subjects with suspected central nervous system malignancy. Patients have a histologically or radiographically confirmed relapsed or refractory solid tumor or primary central nervous system (CNS) malignancy Subjects with symptomatic central nervous system (CNS) disease which is not adequately controlled Uncontrolled central nervous system (CNS) disease (for hematologic malignancies) Have central nervous system disease (CNS) as follows: Active central nervous system (CNS) disease Known primary central nervous system (CNS) malignancy Patients with a history of central nervous system disease must have no clinical or radiological evidence of central nervous system (CNS) disease at the time of protocol enrollment and with CNS toxicity =< grade 2; patients with seizure disorders may be enrolled if seizures are well controlled Presence of active and clinically relevant central nervous system (CNS) disorder; Presence of active and clinically relevant Central Nervous System (CNS) disorder (Bevacizumab-related exclusion) History or evidence upon physical/neurological examination of central nervous system (CNS) disease (e.g. seizures) unrelated to cancer unless adequately treated with standard medical therapy Active central nervous system (CNS) disorder or seizure disorder or known CNS disease or neurologic symptomatology Presence of any significant central nervous system (CNS) or psychiatric disorder(s) that would hamper the patient's compliance; Active central nervous system (CNS) disease in patient with history of CNS malignancy. Active central nervous system (CNS) or extramedullary disease unless approved by the principal investigator (PI) Active central nervous system malignancy Rapidly progressive, clinically unstable central nervous system hematological malignancy. Note: Central nervous system evaluation is only required in subjects with known or suspected central nervous system malignancy. Active, uncontrolled central nervous system (CNS) disease Active central nervous system (CNS) malignancy Eligible for extra-central nervous system (CNS) SAbR to 1-6 sites of disease Active central nervous system (CNS) disease in patient with history of CNS malignancy Active central nervous system malignancy Patients with clinical evidences of active central nervous system (CNS) disease at inclusion Active central nervous system (CNS) disease Suspected AML-related central nervous system involvement; a lumbar puncture (LP) is not required to exclude central nervous system (CNS) disease Presence of any central nervous system tumor that has not been stable for at least 4 weeks off corticosteroids. Patient with active central nervous system (CNS) disease AND (by central assessment) either: Patients with central nervous system disease are eligible for enrollment if they have received prior radiotherapy or surgery to sites of CNS (central nervous system) metastatic disease and are without evidence of clinical progression for at least 12 weeks after therapy Participant has overt central nervous system (CNS) disease (CNS 3 status) Patients with a history of central nervous system disease must not have severe peripheral neuropathy, signs of leukencephalopathy, or active central nervous system (CNS) infection; patients with seizure disorders may be enrolled if seizures are well controlled on anticonvulsant therapy Stable central nervous system (CNS) disease that has been adequately treated and is not under active treatment allowed Patients with active central nervous system (CNS) or epidural tumor Patients with central nervous system (CNS) disease who have received treatment and disease has been stable for four weeks are eligible Active central nervous system (CNS) or extramedullary disease Active central nervous system (CNS) disease. Patients with central nervous system (CNS) tumors who are receiving steroids are eligible Non-central nervous system (CNS) radiotherapy within 1 week prior to C1D1 of study therapy Significant co-morbid central nervous system disease, including but not limited to, multiple sclerosis No active central nervous system (CNS) disease Patients with active central nervous system (CNS) disease Patients may NOT have evidence or symptoms of central nervous system (CNS) disease at the time of enrollment Known chronic or active viral infections of the central nervous system (CNS) Confirmed absence of central nervous system (CNS) disease Active central nervous system (CNS) disease Patients with active central nervous system (CNS) disease Prior history of encephalitis, multiple sclerosis, or other central nervous system (CNS) infection No uncontrolled seizure disorder, active neurological disease, or known central nervous system (CNS) disease Patients with active central nervous system (CNS) or epidural tumor Patients with known malignant disease of the central nervous system. History of primary central nervous system (CNS) disease that would interfere with subject evaluation Patient with active central nervous system (CNS) disease Patient has a primary central nervous system tumor Central nervous system (CNS) tumor refractory to intrathecal chemotherapy and/or cranio-spinal radiation No current central nervous system (CNS) myeloma at time of enrollment Tumors arising outside of the central nervous system (CNS) Any history of disease involving the central nervous system (Part 1). Known active disease involving the central nervous system (Part 2). Presence of central nervous system (CNS) disease Stable central nervous system (CNS) disease that has been adequately treated and is not under active treatment allowed Active central nervous system malignancy Many patients present with concomitant systemic disease outside of the central nervous system; extra-central nervous system (CNS) disease status should meet the following criteria:\r\n* Patients with concomitant systemic disease under control with current or prior systemic treatment, as per primary treating physician\r\n* Patients without any evidence of systemic disease, either receiving systemic treatment or on active observation (Cohort D) Active central nervous system malignancy Patients may have active malignancy outside the central nervous system Subjects with rapidly progressing central nervous system (CNS) disease with associated neurological deterioration Patients with central nervous system (CNS) malignancies. Active central nervous system malignancy Patients with limited disease (if MF/SS: stages IA) or central nervous system (CNS) disease. Active central nervous system (CNS) disease in patient with history of CNS malignancy Concommitant therapy that includes other chemotherapy that is or may be active against ALL (except central nervous system [CNS] therapy) Active central nervous system (CNS) disease Active leukemic central nervous system (CNS) disease Eligible for extra-central nervous system (CNS) SABR to 1-5 sites of disease Central nervous system (CNS) toxicity including peripheral neuropathy =< grade 2 Subject has known current central nervous system (CNS) disease Pre-existing central nervous system (CNS) demyelination or seizure disorders Central nervous system (CNS) toxicity =< grade 2 Patients with active central nervous system (CNS) malignancy Symptomatic leukoencephalopathy, active central nervous system (CNS) malignancy or other neuropsychiatric abnormalities believed to preclude transplantation (previous CNS malignancy, presently in complete remission [CR] is not an exclusion) Patient has chronic or active viral infections of the central nervous system (CNS) Patients with disease progression in the central nervous system (CNS) only Patients with active central nervous system disease or with granulocytic sarcoma as sole site of disease Patients with active central nervous system (CNS) or epidural tumor History of central nervous system (CNS) disease Central nervous system disease as evidence by clinical symptomatology Subjects with known central nervous system disease Primary disease involving the Central Nervous System (CNS) Patients with central nervous system disease are eligible for enrollment if they have received prior radiotherapy or surgery to sites of central nervous system metastatic disease, have been off glucocorticoids for at least 4 weeks, have no overt evidence of neurological deficit and are ? 6 weeks from completion of brain irradiation. Active central nervous system disease. Symptomatic leukoencephalopathy, active central nervous system (CNS) malignancy or other neuropsychiatric abnormalities believed to preclude transplantation Participants with known central nervous system disease History of or active central nervous system (CNS) malignancy Active/symptoms of central nervous system (CNS) disease Evidence for central nervous system (CNS) metastatic disease History or evidence upon physical/neurological examination of central nervous system (CNS) disease unrelated to cancer, unless adequately treated with standard medical therapy (e.g. uncontrolled seizures) Patient has active or history of central nervous system (CNS) disease Adequate central nervous system function defined as:\r\n* Patients with a history of central nervous system (CNS) disease must have no clinical or radiological evidence of CNS disease at the time of study enrollment\r\n* Patients with seizure disorders may be enrolled if seizures are well controlled on anticonvulsants\r\n* CNS toxicity =< grade 2 Active central nervous system (CNS) disease at the time of treatment Active central nervous system (CNS) or symptomatic epidural metastatic disease History of central nervous system (CNS) lymphoma or other CNS disease Known cytopathologically confirmed central nervous system (CNS) infiltration Current central nervous systemic disease No active central nervous system (CNS) disease Subjects with active cancer that has spread to the central nervous system Known central nervous system (CNS) disease Patients with known active central nervous system (CNS) disease History of central nervous system (CNS) thrombotic/embolic or ischemic event(s) Symptomatic central nervous system (CNS) disease. Known active central nervous system (CNS) malignancy Known cytopathologically confirmed central nervous system (CNS) infiltration Significant co-morbid central nervous system disease, including but not limited to, multiple sclerosis Hematologic and primary central nervous system (CNS) malignancies Any primary or active central nervous system (CNS) malignancy, including metastatic disease Central nervous system function defined as not severely somnolent or comatose (central cortical neurotoxicity scale < grade 3) Presence of central nervous system (CNS) metastatic disease History of demyelinating disease or inflammatory disease of the central nervous system or the peripheral nervous system Pathology from the resected brain metastasis must be consistent with a non-central nervous system primary site; Note: patients with or without active disease outside the nervous system are eligible (including patients with unknown primaries), as long as the pathology from the brain is consistent with a non-central nervous system primary site Active central nervous system (CNS) disease Patients with stable, treated central nervous system (CNS) disease are eligible Have active Central Nervous System (CNS) disease Patients with relapse also detected in the central nervous system (CNS) may be treated on this protocol; however, if intrathecal chemotherapy is being administered, T cells should not be administered until at least 24 hours thereafter Active central nervous system (CNS) disease in patient with history of CNS malignancy History or clinically suspicious for cancer-related Central Nervous System disease Patients may have active malignancy outside the central nervous system Central Nervous System (CNS) disease only. Known central nervous system malignancy. Active central nervous system (CNS) disease Active central nervous system (CNS) or extramedullary malignant disease Patients with central nervous system (CNS) disease or testicular disease are eligible Active central nervous system disease (CNS) metastases, as indicated by clinical symptoms, cerebral edema or progressive growth Uncontrolled central nervous system (CNS) disease Known central nervous system (CNS) disease Patients with active central nervous system (CNS) malignancy are not eligible for this trial Active/symptoms of central nervous system (CNS) disease Central nervous system (CNS) disease Primary brain or other central nervous system malignancy. History of central nervous system hemorrhage Active central nervous system (CNS) disease in patient with history of CNS malignancy Patients with documented central nervous system (CNS) disease Severe central nervous system, pulmonary, or renal disease not related to the participant's cancer. Has a history of primary central nervous system malignancy. Patient has no worsening central nervous system symptoms; and Patients with active central nervous system (CNS) disease Known central nervous system disease (e.g., Alzheimer's disease). Patients with a history of central nervous system (CNS) malignancy. Patients with central nervous system disease Has a symptomatic central nervous system (CNS) tumor causing nausea and/or vomiting Patient has active or history of central nervous system (CNS) disease. History of central nervous system (CNS) PTLD Active Central Nervous System [CNS] disease Active central nervous system (CNS) disease b. Central nervous system (CNS) trauma or active seizure disorders requiring medication Primary malignancy of the central nervous system. Patients with active central nervous system (CNS) disease Central nervous system tumors are allowed Patients with documented central nervous system (CNS) ischemia and/or infarction, whether symptomatic or discovered incidentally without clinical symptoms, will be excluded from study participation Active MM involving the central nervous system. Pre-existing central nervous system (CNS) demyelination or seizure disorders Active MM involving the central nervous system (CNS). Active central nervous system lesions Active central nervous system (CNS) disease (related to primary malignancy) at the time of enrollment History of significant central nervous system (CNS) injury or disease predating or unrelated to cancer diagnosis Patient has symptomatic primary or metastatic central nervous system (CNS) disease Patients with active central nervous system (CNS) disease, such as clinically-evident metastases or leptomeningeal disease, dementia, or encephalopathy Patients with history of seizures or uncontrolled central nervous system (CNS) disease, significant hepatic or renal dysfunction Patients with active central nervous system (CNS) disease, such as clinically-evident metastases or leptomeningeal disease, dementia, or encephalopathy. Comorbidities at particular risk (i.e., active central nervous system [CNS], active CNS metastases, hydrocephalus or coagulopathy) History of central nervous system (CNS) tumor Cranial radiotherapy for central nervous system (CNS) leukostasis; History of Grade >= 2 central nervous system (CNS) hemorrhage All patients need to have received at least one prior central nervous system (CNS) directed therapy; there is no restriction on the number of recurrences Participant is currently receiving treatment with benzodiazepines or other central nervous system (CNS) depressants Active central nervous system (CNS) disease Active central nervous system (CNS) disease (the action for acupuncture may be associated with central nervous system activity, and patients with CNS pathology may respond differently to treatment than the general population) Uncontrolled central nervous system (CNS) disease (for hematologic malignancies) Active central nervous system malignancy Non-central nervous system (CNS) malignant disease must be sufficiently controlled so that patient can be without additional systemic therapy for approximately 2 months Subjects with known central nervous system disease Has a symptomatic primary or metastatic central nervous system (CNS) malignancy with nausea and/or vomiting (asymptomatic participants may participate in study) Central nervous system (CNS) only disease on recent imaging MM involving the central nervous system. Diagnosis: Must have MRI documenting a measurable lesion w/in central nervous system consistent with primary central nervous system tumor, for which maximal safe surgical resection is indicated Suspected central nervous system (CNS) tumor(s) or sarcoma.