Inclusion Criteria:

• - Age 12-75 years.

The first 3 subjects will be 18 years of age to gain experience and observe safety. After 3 adult subjects have successfully engrafted and if the safety profile is tolerable, adolescents age 12 may be enrolled on to the trial.

• - Patients with a diagnosis either follicular lymphoma (FL), mantle cell lymphoma (MCL), chronic lymphocytic leukemia (CLL), multiple myeloma (MM), Hodgkin's lymphoma (HL), non-Hodgkin's lymphoma (NHL), chronic myeloid leukemia (CML), myelodysplastic syndrome, myeloproliferative syndromes (MPD), acute myeloid leukemia (AML) or acute lymphoid leukemia (ALL).

• - Patients with aplastic anemia and severe immune deficiency or nonmalignant bone marrow failure states.

Patients with severe thalassemia requiring regular blood transfusions or sickle cell disease with severe clinical features (these include any clinically significant sickle genotype, for example, hemoglobin SS (Hb SS), hemoglobin SC (Hb SC), hemoglobin S beta thalassemia (Hb Sbeta), or Hemoglobin S-OArab genotype] with at least one of the following manifestations:

• - Clinically significant neurologic event (stroke) or neurological deficit lasting > 24 hours; - History of two or more episodes of acute chest syndrome (ACS) in the 2-year period preceding enrollment or referral despite adequate supportive care measures (i.e. asthma therapy); - An average of three or more pain crises per year in the 2-year period preceding enrollment or referral (required intravenous pain management in the outpatient or inpatient hospital setting); - Administration of regular red blood cell (RBC) transfusion therapy, defined as 8 or more transfusion events per year (in the 12 months before enrollment) to prevent vaso-occlusive clinical complications (i.e. pain, stroke, or acute chest syndrome); - An echocardiographic finding of tricuspid valve regurgitant jet (TRJ) velocity >= 2.7 m/sec.

• - Ongoing high impact1 chronic pain on a majority of days per month for >= 6 months as defined as ONE or more of the following: Chronic pain without contributory sickle cell disease (SCD) complications2, OR mixed pain type in which chronic pain is occurring at site(s) (arms, back, chest, or abdominal pain) unrelated to any sites associated with contributory SCD complications2 (e.g. leg ulcers and/or avascular necrosis) - Patients with hematological malignancies must have had persistent or progressive disease despite initial chemotherapy and must have achieved stable disease or a partial or complete response to their most recent chemotherapy.

Patients with low bulk or indolent relapse are eligible without additional treatment. Patients with high risk acute myeloid leukemia by European LeukemiaNet (ELN) criteria in first remission are eligible.

• - Availability of a haploidentical related donor.

• - Karnofsky performance status >= 70%.

• - Left ventricular ejection fraction of at least 40%.

• - Pulmonary function test (PFT) demonstrating an adjusted diffusion capacity of least 50% predicted value for hemoglobin concentration.

• - Serum creatinine =< 1.5 mg/dl.

• - Serum glutamic-pyruvic transaminase (SGPT) =< 200 IU/ml.

• - Bilirubin < 1.5 mg/dl (unless Gilbert's syndrome).

• - Negative pregnancy test in a woman with child bearing potential.

Exclusion Criteria:

• - Human immune deficiency virus (HIV) seropositive.

• - Uncontrolled infection or serious medical or psychiatric condition that would limit tolerance to the protocol treatment.

• - Active central nervous system (CNS) malignancy.

• - Availability of medically eligible, human leukocyte antigen (HLA)-matched related stem cell donor.

PRIMARY OBJECTIVE:

• I. To determine the optimal dose of anti-viral veto cells, defined as the dose which achieves engraftment without severe graft-vs-host disease (GVHD) at 42 days after non-myeloablative megadose T cell depleted haploidentical hematopoietic cell transplantation (HCT).

SECONDARY OBJECTIVES:

• I. Toxicity.

• II. Response rate.

• III. Time to progression.

• IV. Infections.

• V. Immune reconstitution.

• VI. Overall survival up to 1 year.

OUTLINE: This is a dose-escalation study of cytokine-treated veto cells. CONDITIONING REGIMEN: Patients receive anti-thymocyte globulin (ATG) intravenously (IV) over 4 hours on days -9 to -7 and fludarabine IV over 1 hour on days -6 to -3, then undergo total body irradiation (TBI) on day -1. TRANSPLANT: Patients undergo peripheral blood stem cell transplantation (PBSCT) IV over 30-60 minutes on day 0. GVHD PROPHYLAXIS: Patients receive cyclophosphamide IV over 3 hours on days +3 and +4 and cytokine-treated veto cells IV over 30-60 minutes on day +7. After completion of stem cell transplant, patients are followed up once a week for 4 weeks, once a month for 3 months, and then periodically for one year.

Arms

Experimental: Treatment (chemotherapy, PBSCT, cytokine-treated veto cells)

CONDITIONING REGIMEN: Patients receive ATG IV over 4 hours on days -9 to -7, and fludarabine IV over 1 hour on days -6 to -3, then undergo TBI on day -1. TRANSPLANT: Patients undergo PBSCT IV over 30-60 minutes on day 0. GVHD PROPHYLAXIS: Patients receive cyclophosphamide IV over 3 hours on days +3 and +4 and cytokine-treated veto cells IV over 30-60 minutes on day +7.

Interventions

Biological: - Anti-Thymocyte Globulin

Given IV

Drug: - Cyclophosphamide

Given IV

Biological: - Cytokine-treated Veto Cells

Given IV

Drug: - Fludarabine

Given IV

Procedure: - Peripheral Blood Stem Cell Transplantation

Undergo PBSCT

Radiation: - Total-Body Irradiation

Undergo TBI