Intravenous (IV) AMD3100 for Mobilization and Matched Related Transplant for Advanced Hematological Malignancies

Inclusion Criteria: Donor Eligibility * Donor is 18 to 70 years of age inclusive. * If female and of child-bearing age: must be non-pregnant, not breast feeding and agree to use adequate contraception. * Donor is a 6/6 HLA-matched sibling willing to donate PBSC for transplant. * Donor must be willing to provide written informed consent. * Adequate cardiac function with no history of congestive heart failure and no history of atrial fibrillation or ventricular tachyarrhythmia. * Adequate renal function as defined by a calculated serum creatinine clearance of ≥75% of normal (Cockcroft-Gault equation). * Adequate hepatic function as defined by a total bilirubin \<2x normal or absence of hepatic fibrosis/cirrhosis. * Adequate neurologic function as defined by NO evidence of a severe central or peripheral neurologic abnormality. No history of cerebrovascular accident or seizure disorder requiring anticonvulsant medication. * Donor must be HIV-1\&2 antibody and HTLV-I\&II antibody sero-negative, by Food and Drug Administration (FDA) licensed test. * Donor must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. * Donor must demonstrate ability to be compliant with study regimen. * Donor must not have an active infection at the time of study entry. * Donor does not have active alcohol or substance abuse within 6 months of study entry. * Donor is not currently enrolled on another investigational agent study. * Donor does not have any medical condition, which, in the opinion of the clinical investigator, would interfere with his/her evaluation. Recipient Eligibility * Recipient must have available the successful collection of an AMD3100 mobilized product. When an adequate collection cannot be obtained using G-CSF, some recipients may need to receive a combined product of mobilized cells with AMD3100 and g granulocyte-colony stimulating factor (G-CSF). Recipients who receive less than 2.0 X 106 CD34+ cells/kg/actual recipient weight after two days of IV AMD3100 will not be considered "eligible" but followed per protocol for safety purposes only. * Patient is 18 to 65 years of age inclusive. * Patient is willing and has a 6/6 HLA-matched sibling willing to donate PBSC for transplant. * Patient must provide signed informed consent. * If female and of child-bearing age: must be non-pregnant, not breast feeding, and uses adequate contraception. * Patient must have one of the following diagnoses: * Acute myelogenous leukemia (AML) in 1st or subsequent remission or in relapse, * Acute lymphoblastic leukemia (ALL) in 1st or subsequent remission or in relapse, * Myelodysplastic syndrome either intermediate 1 or 2, or high risk by the International Prognostic Scoring System, * Chronic myelogenous leukemia (CML) in accelerated or second chronic phase, * Non-Hodgkin's lymphoma (NHL) or Hodgkin's disease (HD) in 2nd or greater complete remission, partial remission, or refractory relapse, * Chronic lymphocytic leukemia (CLL), Rai Stage 2-4, failing at least 2 prior regimens, OR * Multiple myeloma (MM), Stage 2-3. * Adequate cardiac function with a left ventricular ejection fraction ≥ 40%. * Adequate pulmonary function defined as NO severe or symptomatic restrictive or obstructive lung disease, and formal pulmonary function testing showing an FEV1 ≥50% of predicted and a DLCO ≥40% of predicted, corrected for hemoglobin. * Adequate renal function as defined by a serum creatinine clearance of ≥75% of normal (Cockcroft-Gault equation). * Adequate hepatic function as defined by a total bilirubin \<2x normal or absence of hepatic fibrosis/cirrhosis. * Adequate neurologic function as defined by NO evidence of a severe central or peripheral neurologic abnormality. Patients with a history of previous central nervous system (CNS) tumor involvement are eligible provided they are without symptoms or signs and the CNS is now free of disease on lumbar puncture and CT scan of the brain. * No evidence of active infection at the time of the transplant preparative regimen or at time of transplantation. * Patient must be HIV-1\&2 antibody and HTLV-I \& II antibody sero-negative, by FDA licensed test. * Patient has an ECOG performance status of 0 or 1. * Patient must demonstrate ability to be compliant with medical regimen. * Patient must not have active alcohol or substance abuse within 6 months of study entry. * Patient must not be enrolled on another investigational agent concurrently. * Patient must not have any medical condition, which, in the opinion of the clinical investigator, would interfere with the evaluation of the patient. Exclusion Criteria: * See Inclusion criteria above