Patients with the following will be ineligible for registration onto this study: Study entry PSA should not be obtained during the following time frames: \r\n* 10-day period following prostate biopsy\r\n* Following initiation of hormonal therapy\r\n* Within 30 days after discontinuation of finasteride\r\n* Within 90 days after discontinuation of dutasteride The following diagnoses are to be included: PhaseII : Prior treatment with any of the following agents: If sexually active female, patient must be/have one of the following: Have at least one of the following: Meets one of the sets of the following criteria: Either of the following: Any of the following: For salivary duct carcinoma patients, the following are required: Treatment with any of the following: Patients must have available two UCB units fulfilling the following criteria: One of the following: Patients must fulfill one of the following: Treatment with any of the following: Any of the following cardiac criteria: For subjects with TH-FL: relapsed or refractory disease following at least 2 prior regimens or following an auto-HSCT. At least 1 prior regimen with an anti-CD20 mAb in combination with chemotherapy is required following documented transformation Treatment with any of the following: Any of the following cardiac criteria: Disease Status: Patients must have ONE of the following: Tumor: patient must have one of the following diagnoses to be eligible: All subjects must fulfill one of the following: Any of the following cardiac criteria: Dose Expansion Portion: Patients must satisfy one of the following criteria: Treatment with chronic immunosuppressants (e.g., cyclosporine following transplantation) Has received treatment with any of the following: for subjects with TH-FL: relapsed or refractory disease following at least 2 prior regimens or following an auto-HSCT. At least 1 prior regimen with an anti-CD20 mAb in combination with chemotherapy is required following documented transformation Any one of the following: Use of the following: Disease status must be 1 of the following: Any of the following cardiac criteria: Patients must have either of the following: Treatment with any of the following: Any of the following cardiac criteria: Use or consumption of any of the following substances: Each patient must satisfy at least one of the following criteria: Patient must also satisfy at least one of the following criteria: Patient must also satisfy at least one of the following criteria: Study entry PSA should not be obtained during the following time frames: (1) 10-day period following prostate biopsy; (2) following initiation of hormonal therapy; (3) within 30 days after discontinuation of finasteride; (4) within 90 days after discontinuation of dutasteride Combination of any two of the following (a+b or a+c, or b+c): Have one of the following documented by a local test: Have one of the following documented by a local test: The combination of any 2 of the following methods when both are used simultaneously: (Monotherapy - Parts A, B, C, D, G, H, J, and K) -- Relapsed, refractory, or progressive disease, specifically: (a) Solid tumors: Following at least 1 prior systemic therapy, and no further standard therapy is available for the patient's advanced solid tumor at the time of enrollment; or (b) Classical HL: Following at least 2 prior systemic therapies in patients who are not candidates for autologous stem cell transplant (SCT), or following failure of autologous SCT; or (c) DLBCL: Following at least 1 prior systemic therapy; patients must have also received intensive salvage therapy unless they refused or were deemed ineligible; or (d) Indolent lymphoma: Following at least 1 prior chemoimmunotherapy regimen that included an anti-CD20 monoclonal antibody and for which no other more appropriate treatment option exists Study entry PSA and serum testosterone must not be obtained during the following time frames: (1) 10-day period following prostate biopsy; (2) following initiation of oral androgen manipulation; (3) within 30 days after discontinuation of finasteride or dutasteride Has either of the following: Any of the following cardiac criteria: Subjects must satisfy the following criteria to be enrolled in the study: Use of a combination of any two of the following (a+b or a+c, or b+c): Patients with either of the following diagnoses: Patients must satisfy 1 of the following criteria for prior therapy: At least one of the following indications for treatment: Subjects must satisfy the following criteria to be enrolled in the study: The following medications are excluded: The following medications are excluded: Treatment with any of the following: Subjects must satisfy the following criteria to be enrolled into the study: one or more of the following Myeloma-related organ dysfunction (at least one of the following); one or more of the following biomarkers of malignancy: The following medications are excluded: Indication for treatment consistent with IWCLL criteria, i.e. at least one of the following criteria should be met Prior treatment with the following: Subjects must satisfy the following criteria to be enrolled in the study: Have any history of the following: Must have significant residual invasive disease at the time of definitive surgery following preoperative chemotherapy. Significant residual disease is defined at least one of the following: History of prior therapy that satisfies one of the following criteria: Treatment with any of the following: Any of the following cardiac criteria: One of the following acceptable forms of contraception is required: Treatment with any of the following: Any of the following cardiac criteria: Must have significant residual invasive disease at the time of definitive surgery following preoperative chemotherapy. Significant residual disease is defined as at least one of the following: Patient must have one of the following: Depending upon patient prior treatment the following apply: Resistant to or intolerant of hydroxyurea, that is, fulfilling at least 1 of the following criteria: Diagnosed with one of the following diseases: One of the following is required: One of the following is required: Satisfy at least one of the following criteria Have either of the following diagnoses: Patients must have one of the following: Treatment with chronic immunosuppressants (e.g., cyclosporine following transplantation) Patients with Ph+ B-precursor ALL, with any of the following: Treatment with chronic immunosuppressants (e.g., cyclosporine following transplantation) Recipient must have one of the following diagnoses: Recipient must not have had (the following therapies within the following timeframe): Vital signs criteria defined as 3 or more of the following at Baseline: One or more of the following indications for treatment: presence of at least one of the following B-symptoms: All patients must have completed therapy including intensive induction followed by ASCT and radiotherapy to be eligible for ANBL0032; radiotherapy may be waived for patients who either have small adrenal masses which are completely resected up front, or who never have an identifiable primary tumor; examples of such therapies include: \r\n* Following treatment per A3973 protocol\r\n* Following treatment per Pediatric Oncology Group (POG)-9341/9342 protocol\r\n* Following treatment per CCG3891\r\n* Following treatment on New Approaches to Neuroblastoma Therapy (NANT) 2001-02\r\n* Enrollment on or following treatment per ANBL02P1\r\n* Enrollment on or following treatment per ANBL07P1\r\n* Tandem transplant patients are eligible: \r\n** Following treatment on or per ANBL0532\r\n** Following treatment per POG 9640\r\n** Following treatment per COG ANBL00P1\r\n** Following treatment per CHP 594/Dana-Farber Cancer Institute (DFCI) 34-DAT Subject has received or plans to receive the following therapy/treatment within the following periods prior to leukapheresis or lymphodepleting chemotherapy: Has all of the following: Patients with any of the following are not eligible: Use of the following: Exposure to any of the following: hospitalized with one of the following At least one of the following: Treatment with any of the following: Patients are to be excluded from the study if they have any of the following: Use of a combination of any two of the following: TKI treatment failure will be defined as 1 of the following: Intolerance to TKI therapy will be defined as 1 of the following: Use or consumption of any of the following substances: Use or consumption of any of the following substances: