Cord Blood (CB) Ex-vivo Mesenchymal Stem Cell (MSC) Expansion + Fucosylation

Inclusion Criteria:

1. Patients must have one of the following hematologic malignancies: a. Acute Myelogenous
Leukemia (AML), induction failure, high-risk for relapse first remission (with
intermediate-risk or high-risk cytogenetics, flt3 mutation positive and/or evidence of
minimal residual disease by flow cytometry), secondary leukemia from prior
chemotherapy and/or arising from MDS, Langerhan's cell histiocytosis, any disease
beyond first remission.

2. (#1, continued) b. Myelodysplastic Syndrome (MDS): MDS IPSS INT-1 will be enrolled
only if the subjects have failed previous leukemia treatments and are
transfusion-dependent. MDS may be primary or therapy related, including patients that
will be considered for transplant. Including the following categories: 1) revised IPSS
intermediate and high risk groups, 2) MDS with transfusion dependency, 3) failure to
respond or progression of disease on hypomethylating agents, 4) refractory anemia with
excess of blasts, 5) transformation to acute leukemia, 6) chronic myelomonocytic
leukemia, 7) atypical MDS/myeloproliferative syndromes, 8) complex karyotype, abn(3g),
-5/5g-, -7/7g-, abn(12p), abn(17p).

3. (#1, continued) c. Acute Lymphoblastic Leukemia (ALL) patients with the following will
be considered: Induction failure, primary refractory to treatment (do not achieve
complete remission after first course of therapy) or are beyond first remission
including second or greater remission or active disease. Patients in first remission
are eligible if they are considered high risk, defined as any of the following
detected at any time: with translocations 9;22 or 4;11, hypodiploidy, complex
karyotype, secondary leukemia developing after cytotoxic drug exposure, and/or
evidence of minimal residual disease, or acute biphenotypic leukemia which excludes >
7 chromosomal abnormalities, or double hit non-Hodgkin's lymphoma.

4. (#1, continued) d. Non-Hodgkin's Lymphoma (NHL) in second or third complete remission
or relapse (including relapse post autologous hematopoietic stem cell transplant), or
relapsed double hit lymphoma.

5. (#1, continued) e. Small Lymphocytic Lymphoma (SLL), or Chronic Lymphocytic Leukemia
(CLL) with progressive disease with progression after standard of care therapy or have
failed/been intolerant to ibrutinib.

6. (#1, continued) f. CML second chronic phase or accelerated phase.

7. (#1, continued) g. Hodgkin's Disease (HD): Induction failure after the first complete
remission, or relapse (including relapse post autologous hematopoietic stem cell
transplant), or those with active disease.

8. The first 6 patients must be >/= 18 and include pediatric patients >/= 12 and patients will be determined in conjunction with an MDACC pediatrician.

9. Performance score of at least 80% by Karnofsky or PS < 3 (ECOG) (age >/= 12 years).

10. Adequate major organ system function as demonstrated by: a. Left ventricular ejection
fraction of > 40%; b. Pulmonary function test (PFT) demonstrating a diffusion capacity
of least 50% predicted. c. Creatinine older and normal.

11. Negative Beta HCG test in a woman with child bearing potential defined as not
post-menopausal for 12 months or no previous surgical sterilization and willing to use
an effective contraceptive measure while on study.

12. Patients must have two CB units available which are matched with the patient at 4, 5,
or 6/6 HLA class I (serological) and II (molecular) antigens. Each cord must contain
at least 1.5 x 10^7 total nucleated cells/Kg recipient body weight (pre-thaw).

13. Have identified a back up cells source in case of engraftment failure. The source can
be autologous, related or unrelated.

14. Patient must not have a 10/10 HLA matched family member or unrelated donor.

15. Patients will have a back-up graft from any of the following: an available fraction of
autologous marrow; or PBPCs harvested and cryopreserved; or family member donor; or a
third cord blood unit.

16. Prior to initiating chemotherapy in this study, twenty-one or more days must have
elapsed since the patient's last radiation or chemotherapy administration (Hydrea,
Gleevec and other TKI inhibitors as well as intra-thecal therapy are accepted
exceptions).

Exclusion Criteria:

1. Patients with known history of HIV/AIDS.

2. Patients with positive hepatitis serology that is definitive of active disease.

3. Active CNS disease in patient with history of CNS malignancy.

4. Patients with chronic active hepatitis or cirrhosis. If positive hepatitis serology,
the Study Chair may deem the patient eligible based on the results of liver biopsy.

5. Patients with uncontrolled serious medical condition such as persistent septicemia
despite adequate antibiotic therapy, decompensated congestive heart failure despite
cardiac medications or pulmonary insufficiency requiring intubation (excluding primary
disease for which CB transplantation is proposed), or psychiatric condition that would
limit informed consent.

6. Positive beta HCG in female of child-bearing potential defined as not post-menopausal
for 12 months or no previous surgical sterilization or breast-feeding.

7. Pediatric patients with acute lymphoblastic leukemia (ALL) that is t (9,22) positive
in first remission are not eligible unless there is evidence of minimal residual
disease after initial induction and/or consolidation treatment or the pediatric Ph+
ALL is clinically refractory to available therapies with evidence of persistence in
the bone marrow or peripheral blood.

8. Patients with options for treatment that are known to be curative are not eligible.