Bioengineered Allogeneic Immune Cells (AlloStim) Not Requiring HLA Donor Match for Blood Cancers

Inclusion Criteria: * Histologically confirmed hematological malignancy of 1 of the following types: * Acute Myeloid Leukemia (AML) meeting the following criteria: * Relapsed or primary refractory disease with ≤ 10% blasts in the peripheral blood and ≤ 20% blasts in the bone marrow. * Acute Lymphoblastic Leukemia (ALL) meeting the following criteria: * Relapsed or primarily refractory disease with ≤ 10% blasts in the peripheral blood and ≤ 20% blasts in the bone marrow * Chronic Myeloid Leukemia (CML)\* with an inadequate response to imatinib meeting 1 of the following criteria: * Second or subsequent chronic phase * Accelerated phase \[\*Patients with CML in blast crisis (\> 30% promyelocytes and myeloblasts in the bone marrow) are not eligible\] * Non-Hodgkin's Lymphoma (NHL) including Mantle Cell Lymphoma (MCL) meeting 1 of the following criteria: * Primary refractory disease or in refractory relapse * Relapsed disease after autologous stem cell transplantation * Chemosensitive relapsed disease without CR to standard salvage therapy AND no option for autologous stem cell transplantation due to blood or marrow involvement or failure to harvest sufficient autologous stem cells. * Chronic Lymphocytic Leukemia (CLL) meeting both of the following criteria: * Stage III or IV disease * Refractory to fludarabine, Rituxan® and Campath® or refuses * Multiple Myeloma (MM) meeting 1 of the following criteria: * Primary refractory disease or in refractory relapse * Relapsed disease after autologous stem cell transplantation * Hodgkin's Disease * Relapsed after prior autologous transplant or after 2 or more combination chemotherapy regimens and ineligible for autologous stem cell transplant. * EBV driven lymphoproliferative disorders in immunocompetent patients progressing despite standard therapies, including: * T-cell Non-Hodgkin's Lymphoma * Burkitt's Lymphoma * EBV+ Hodgkin's Disease * Ability to comprehend the investigational nature of the study and provide informed consent. * Measurable or evaluable disease * Eastern Cooperative Oncology Group (ECOG) performance status of \<2. * Age 18 years or older * Expected survival 6 months or longer * No radiation or chemotherapy in previous 2 weeks * No immunotherapy in the previous 4 weeks * Absence of active infection within 2 weeks * Adequate hepatic function, with total bilirubin level less than 1.2 times the upper limit of normal (ULN) and aspartate and alanine aminotransferase levels less than 2.5 times the ULN prior to infusion * Adequate bone marrow function defined as a white blood cell count of at least 2 x 109/L (2000/µL), absolute neutrophil count of at least 1 x 109/L (1000/µL), hemoglobin level of at least 80 g/L (8.0 g/dL), and a platelet count of at least 50 x 109/L (50,000/µL) priot to infusion. Patients who are transfusion- or growth factor-dependent are allowed, provided these values could be achieved with transfusion. * Adequate cardiovascular function defined as no ischemia, no new conduction system abnormalities, no class 3 or 4 New York Heart Association congestive heart failure, and no myocardial infarction in the previous 6 months. A ≥45% left ventricular ejection fraction (LVEF) required in the previous 6 months. * Adequate kidney function defined as serum creatinine level 1.5 mg/dL or less, or an estimated creatinine clearance level of at least 60 mL/min prior to infusion. * Adequate lung function defined as pulse oxymetry greater than or equal to 92% on room air prior to infusion, DLco≥50%, FEV1 and FVC ≥50% within 2 weeks * No known allergy to murine products or HAMA testing results within normal limits * No known allergy to bovine products Exclusion Criteria: * No pregnancy or breast feeding * No known human immunodeficiency virus (HIV+) * No seropositivity or active viral hepatitis (HBV+, HCV+) * No prior allogeneic transplant (cell or organ) * No serious concomitant medical or psychiatric conditions that could interfere with treatment. * No EBV-induced lymphomas associated with immunosuppression, including patients with iatrogenic immunodeficiencies (such as organ transplant) or HIV-related immunodefiency. * No chronic myelogenous leukemia in blast crisis. * No myelodysplastic syndromes with refractory anemia