Cord Blood Fucosylation to Enhance Homing and Engraftment in Patients With Hematologic Malignancies

140 mg/m2 by vein on Day -2 only for Fludarabine + Melphalan group.

10 mg/m2 by vein on Days -7 to -4 for Melphalan + Thiotepa + Fludarabine group, or 40 mg on Days -5 to -2 for Fludarabine + Melphalan group.

15 mg/kg (actual body weight with a maximum dose of 1 gram twice daily) by vein or by mouth twice a day from Days -3 to +100 in the absence of Graft vs Host Disease (GvHD).

Starting dose 0.03 mg/kg or 0.015 mg/kg (ideal body weight) by vein starting on Day -2 and tapered around Day +180 if no Graft vs Host Disease (GvHD) is present.

Cord blood infusion on Day 0. Each participant will receive cells from one unexpanded cord blood sample plus cells from a second cord blood sample that has undergone fucosylation.

375 mg/m\^2 by vein on Day -10 for B cell malignancy.

"1.25 mg/Kg by vein on Day -4.~1.75 mg/Kg by vein on Day -3."

Busulfan per standard of care, test dose either as an outpatient prior to admission or as an inpatient on Day -9. Busulfan pharmacokinetics performed with test dose and the first dose on Day -7 per standard of care. Doses of Days -5 and -4 subsequently adjusted to target an AUC of 4,000 microMol.min-1.

30 mg/m\^2 IV Day -7 to Day -4;

2 Gy in AM of Day -3.