Hematopoietic Stem Cell Transplantation (HSCT) Using CD34 Selected Mismatched Related Donor and One Umbilical Cord Unit

Inclusion Criteria:

* Patients between 18 and 65 years old
* Patient has a related family member(haploidentical) or unrelated which is 5 of 10 HLA identical match.

Standard Risk

* Acute myelogenous leukemia: CR1 with high risk cytogenetics or molecular abnormalities such as FLT-3 ITD, or CR2 with a first remission that must have lasted \> 1 year.
* Acute Lymphocytic Leukemia: CR1, in order to be standard risk must NOT have Philadelphia Chromosome.
* Chronic lymphocytic leukemia/small lymphocytic lymphoma (CLL/SLL): Must be refractory to fludarabine or fail to have a complete or partial response after therapy with a regimen containing fludarabine (or another nucleoside analog, e.g. 2-CDA, pentostatin) or experience disease relapse within 12 months after completing therapy with a regimen containing fludarabine (or another nucleoside analog).
* Chronic myelogenous leukemia: resistant to or intolerant of TKI, in CP1 or CP2, or with a mutation that suggests resistance to TKI.
* Myelodysplastic Syndrome: RA, RARS, must be IPSS ≥ INT-2, Blasts \<5%.

High Risk Patients:

* Acute myelogenous leukemia: Patients with CR2 are considered high risk if they have high risk cytogenetics, or molecular abnormalities or CR1 lasted for less than 1 year. Any evidence of active disease or no blasts in an acellular marrow.
* Acute Lymphocytic Leukemia: CR1- with Ph+ disease, CR2/+ with any cytogenetics. Any evidence of active disease.
* Chronic myelogenous leukemia- CP2/+, AP1/+, resistant or intolerant to TKI.
* Hodgkin's or Non Hodgkin's lymphoma- Disease recurrence following an autologous transplant, or high risk disease not thought to benefit from autologous transplant.
* Chronic lymphocytic leukemia- that is resistant to fludarabine, and never has been in remission or with stable disease/progressive disease
* Multiple myeloma: Must have had prior treatment. Patients in CR2 or greater can be considered, must have already failed autologous transplant Previous autologous transplant,must have been greater than 6 months prior to undergoing this transplant.
* Myelodysplastic syndrome: RAEB
* Other Myeloproliferative disorders including myelofibrosis, spent phase p Vera,Essential thrombocytosis,CMML.

Exclusion Criteria:

* Patients \<18 years old Disease related criteria
* APML, presence of t(15,17) in first CR
* Patients with good risk AML, for example t(8;21), or inv 16, or normal cytogenetics with FLT-3-ITD negative, NPM-1 positive disease in 1st CR
* MDS IPSS \< INT-2 Miscellaneous Criteria
* Recipients who have a matched related sibling or unrelated donor
* If recipient has evidence of anti-HLA antibodies directed against cord or haplo-donor as determined byflowPRA.

Underlying health criteria:

* Zubrod performance status \> 2 (see Appendix E)
* Life expectancy is limited to less than 8 weeks by concomitant illness
* Patients with severely decreased LVEF (EF \< 40%)
* Impaired pulmonary function tests (PFT's) (FVC, FEV1, DLCO \< 45% predicted)
* Estimated Creatinine Clearance \<50 ml/min
* Serum bilirubin\> 2.0 mg/dl or SGPT \>3 x upper limit of normal
* Evidence of chronic active hepatitis or cirrhosis
* HIV-positive
* Patient is pregnant
* Patient or guardian not able to provide informed consent