Efficacy Study of T Cell Depleted Allogeneic Non-myeloablative Stem Cell Transplant

Recipient Inclusion Criteria:

* Subjects must have their diagnosis confirmed at the transplant center.
* Performance status must be Cancer and Leukemia Group B (CALGB) = 0, 1, or 2.
* Subjects must have a 3-6/6 human leukocyte antigen (HLA)-matched related donor or 8/8 or better allele level match matched unrelated donor (MUD) (at A,B, C, DRB1, DQ).
* HIV negative.
* Women of child bearing potential must have a negative pregnancy test within 1 week of starting therapy.
* Subjects \> or equal to 18 years of age are eligible.
* Subjects must have a Multi Gated Acquisition Scan (MUGA) and/or Echocardiography (ECHO) or cardiac magnetic resonance (MR) and or diffusing capacity testing of the lung for carbon monoxide (DLCO) performed before transplant.
* Specific populations:

  * Group A) Subjects with a high chance of progressive lymphoid or myelomatous diseases.
  * Group B) Subjects with a high chance of progressive myeloid diseases, marrow failure syndromes or myeloproliferative disorders

Recipient Exclusion Criteria:

* Pregnant or lactating women.
* Subjects with other major medical or psychiatric illnesses which the treating physician feels could seriously compromise tolerance to this protocol.
* Subjects with uncontrolled, progressive infections.
* Subjects who are good candidates for long term disease control with standard chemotherapy or radiation or high dose therapy and autologous support.
* Subjects with active central nervous system (CNS) disease.

Donor Inclusion Criteria:

1. Donor must be capable of providing informed consent. If 14-17 years of age, a 'single patient exemption' from the local Institutional Review Board must be obtained.
2. Donor must not have any medical condition which would make mobilization or apheresis more than a minimal risk, and should have the following:

   1. Adequate cardiac function by history and physical examination. Those with a history of cardiac failure or infarction should be evaluated by a cardiologist prior to donation
   2. Adequate hematopoietic function with hematocrit ≥ 30%, white blood cell count of 3000, and platelets 100,000.
3. Females should not be pregnant or lactating and have a negative serum pregnancy test within 1 week of beginning mobilization if of child bearing potential.