Inclusion Criteria:

        PART 1:

          -  PART 1: Disease criteria

               -  Diagnosis of primary MF (PMF) as defined by the 2008 World Health Organization
                  classification system or diagnosis of secondary MF as defined by the
                  International Working Group (IWG) for Myeloproliferative Neoplasms Research and
                  Treatment criteria

               -  Patients meeting the criteria for intermediate-1, intermediate-2 or high-risk
                  disease by the Dynamic International Prognostic Scoring System (DIPSS) or
                  DIPSS-plus scoring system

          -  PART 1: Ability to understand and the willingness to sign a written informed consent
             document

          -  PART 1: Patient must be a potential hematopoietic stem cell transplant candidate

        PART 2:

          -  PART 2: Meeting criteria for 1st phase as above, at time of initiation of JAK
             inhibitor, including ability to understand and willingness to sign a written informed
             consent; patients arriving to our institution for transplant and not enrolled in Part
             1 may still be enrolled in Part 2 if Part 1 criteria met; these patients will have
             Part 1 endpoints transcribed from medical records

          -  PART 2: Received ruxolitinib for at least 8 weeks immediately prior to conditioning
             and be able to continue until Day -4 pre-transplant

          -  PART 2: Performance status score

               -  Karnofsky >= 70

          -  PART 2: Calculated creatinine clearance using the Cockcroft-Gault formula or 24 hr
             urine creatinine clearance must be > 60 ml/min

          -  PART 2: Total serum bilirubin must be < 3 mg/dL unless the elevation is thought to be
             due to Gilbert's disease or hemolysis

          -  PART 2: Transaminases must be < 3 x the upper limit of normal

          -  PART 2: Patients with clinical or laboratory evidence of liver disease will be
             evaluated for the cause of liver disease, its clinical severity in terms of liver
             function, and the degree of portal hypertension; patients with fulminant liver
             failure, cirrhosis with evidence of portal hypertension or bridging fibrosis,
             alcoholic hepatitis, hepatic encephalopathy, or correctable hepatic synthetic
             dysfunction evidenced by prolongation of the prothrombin time, ascites related to
             portal hypertension, bacterial or fungal abscess, biliary obstruction, chronic viral
             hepatitis with total serum bilirubin > 3 mg/dL, and symptomatic biliary disease will
             be excluded

          -  PART 2: Diffusing capacity of the lung for carbon monoxide (DLCO) corrected > 60%
             normal

               -  May not be on supplemental oxygen

          -  PART 2: Left ventricular ejection fraction > 40% OR

          -  PART 2: Shortening fraction > 26%

          -  PART 2: Comorbidity Index < 5 at the time of pre-transplant evaluation

        DONOR:

          -  DONOR: Human leukocyte antigen (HLA)-matched or 1 antigen mismatched sibling donor

          -  DONOR: 10 of 10 HLA-matched or 1 allele mismatched (9 of 10) unrelated donor

          -  DONOR: Peripheral blood is preferred over bone marrow for non-umbilical cord blood
             recipients

          -  DONOR: Umbilical cord blood units will be selected according to the following
             umbilical cord blood graft selection criteria; one or 2 cord blood (CB) units may be
             used to achieve the required cell dose

          -  DONOR: The CB graft(s) must be matched at 4-6 HLA-A, B, DR Beta 1 (DRB1) loci with the
             recipient and therefore may include 0-2 mismatches at the A or B or DRB1 loci; unit
             selection will be based on cryopreserved nucleated cell dose and intermediate
             resolution A, B antigen and DRB1 allele typing for determination of HLA-match; while
             HLA-C antigen/allele level typing is not considered in the matching criteria, if
             available, it may be used to optimize unit selection

          -  DONOR: Selection of two CB units is allowed to provide sufficient cell dose (see below
             for algorithm to determine single versus double unit transplant); when multiple units
             are selected, the following rules apply:

               -  The CB unit with the least HLA disparity (with the patient) will be selected
                  first (i.e., selection priority is 6/6 match > 5/6 match > 4/6 match); additional
                  CB units then may be selected to achieve the required cell dose, as outlined
                  below; if a second unit is required, this unit will be the unit that most closely
                  HLA matches the patient and meets minimum size criteria outlined below of at
                  least 1.5 x 10^7 total nucleated cells (TNC)/kg (i.e. a smaller, more closely
                  matched unit will be selected over a larger, less well matched unit as long as
                  minimum criteria are met)

               -  If two CB units are used:

                    -  The total cell dose of the combined units must be at least 3.0 x 10^7 TNC
                       per kilogram recipient weight

                    -  Each CB unit MUST contain at least 1.5 x 10^7 TNC per kilogram recipient
                       weight

               -  Algorithm for determining single versus double unit cord blood transplant:

                    -  Match grade 6/6: TNC dose >= 2.5 x 10^7/kg

                    -  Match grade 5/6, 4/6: TNC dose >= 4.0 (+/- 0.5) x 10^7/kg

          -  DONOR: General comments:

               -  Units will be selected first based on the TNC dose and HLA matching

               -  Cluster of differentiation (CD)34+ cell dose will not be used for unit selection
                  unless 2 units of equal HLA-match grade are available; in this case, the unit
                  with the larger CD34+ cell dose (if data available) should be selected

               -  A CB unit that is 5/6 mismatched but homozygous at the locus of mismatch should
                  be chosen over a 5/6 unit with bidirectional mismatch even if the latter unit is
                  larger (has more cells); this also applies to 4/6 units; this is only applicable
                  to choosing units within a given match grade

               -  Other factors to be considered:

                    -  Within the same HLA match grade, matching at DR takes preference

                    -  Cord blood banks located in the United States are preferred

               -  Up to 5% of the cord blood product(s), when ready for infusion, may be withheld
                  for research purposes as long as thresholds for infused TNC dose are met; these
                  products will be used to conduct studies involving the kinetics of engraftment
                  and immunobiology of double cord transplantation

        Exclusion Criteria:

        PART 1:

          -  PART 1: Evidence of human immunodeficiency virus (HIV) infection or known HIV positive
             serology

          -  PART 1: Uncontrolled viral, bacterial, or fungal infections at the time of study
             enrollment

          -  PART 1: History of prior allogeneic transplant

          -  PART 1: Pregnant or breastfeeding (only if patients have not been started on
             ruxolitinib [Rux] by their primary oncologist prior to enrollment)

        PART 2:

          -  PART 2: Uncontrolled viral or bacterial infection at the time of study enrollment

          -  PART 2: Active or recent (prior 6 month) invasive fungal infection without infectious
             disease (ID) consult and approval

          -  PART 2: History of HIV infection

          -  PART 2: Pregnant or breastfeeding

          -  PART 2: Patients without an HLA-identical or 1-allele-mismatched related donor or
             unrelated donor or umbilical cord blood units that meet transplant criteria