Immunoablative Mini Transplant (Hematopoietic Peripheral Blood Stem Cell Transplant [HPBSC])

Inclusion Criteria: Patients with recurrent solid tumors Patients with malignant melanoma Patients with hematological malignancies. Chronic myelogenous leukemia in chronic or accelerated phase, to include chronic myelomonocytic leukemia (juvenile chronic myelogenous leukemia (JCML) or CMML). Acute lymphoblastic leukemia (ALL) First remission high-risk ALL (Ph+ with initial high white blood cell (WBC)t (4-11) in infants less than 1 year and CALLA negative) Second or subsequent remission ALL or isolated extramedullary disease on or off therapy. Acute non-lymphocytic leukemia (ANLL) Patients with ANLL in first remission who have a matched sibling donor. ANLL in second remission, or patients who only achieve an initial partial remission < 15% blasts, or early relapse. Myelodysplastic syndromes (MDS): refractory anemia (RA), refractory anemia with excess blasts (RAEB), refractory anemia with excess blasts in transformation (RAEB-T) and CMML/JCML. Selected immunodeficiencies: Wiskott-Aldrich syndrome. Severe combined immunodeficiency variants that require ablation. Hyper-Immunoglobulin M (IgM) syndrome. Other immune deficiencies after approval from the medical director. Bone marrow failure syndromes (single or multiple hematopoietic lines) Venous access: A double lumen central vascular access device or its equivalent will be required for all patients entered on the protocol. Informed consent: The donor and the patient and/or the patient's legally authorized guardian must acknowledge in writing that consent to become a study subject has been obtained in accordance with the institutional policy approved by the United States (U.S.) Department of Health and Human Services. Patient organ function requirements: Adequate renal function: serum creatinine < 2 x normal, or creatinine clearance calculated by Schwartz formula, of glomerular filtration rate (GFR) > 40 ml/min/1.73m2, or an equivalent GFR as determined by the institutional normal range. Adequate liver function: total bilirubin </= 2 x normal; and Aspartate aminotransferase (AST) or Alanine aminotransferase (ALT) </= 4 x normal. Adequate cardiac function: shortening fraction of > 24% by echocardiogram, or ejection fraction of > 30% by radionuclide angiogram. Adequate pulmonary function: Diffusion Lung Capacity Carbon Monoxide (DLCO), Forced Expiratory Volume in 1 second (FEV1) / Forced Vital Capacity (FVC) > 30% by pulmonary function test. For children who are uncooperative for pulmonary function tests and have no evidence of dyspnea at rest or exercise intolerance, pulse oximetry > 94% on room air is considered acceptable. Performance status: Lansky Score >/= 60% for children </= 16 years of age; or Karnofsky > 60% status for those > 16 years of age. Exclusion Criteria: Patients who are pregnant Inability to find a suitable donor for the patient Patient is HIV-positive Patient has active Hepatitis B Disease progression or relapse prior to HPC infusion