Inclusion Criteria:

          -  Evaluable myelofibrosis by IWG-MRT criteria including one or more of the following:

               -  Spleen >= 5 cm below the left costal margin

               -  MPN-SAF total symptom score (TSS) > 10 at baseline

               -  Hemoglobin < 10 g/dL

          -  Confirmed diagnosis of myelofibrosis (primary myelofibrosis or myelofibrosis secondary
             to essential thrombocythemia or polycythemia vera) by World Health Organization (WHO)
             diagnostic criteria (3 major and 2 minor criteria: major criteria: megakaryocyte
             proliferation and atypia with either reticulin and/or collagen fibrosis, not meeting
             criteria for chronic myelogenous leukemia [CML], polycythemia vera [PV],
             myelodysplastic syndrome [MDS], or other myeloid neoplasm, JAK2V617F or other clonal
             marker or no evidence of reactive marrow fibrosis; minor criteria:
             leukoerythroblastosis, increased lactate dehydrogenase [LDH], anemia, palpable
             splenomegaly)

          -  For cohort 1: early stage MF (low or intermediate 1 stage as defined by Dynamic
             International Prognostic Scoring System [DIPSS]) without currently available treatment
             options

          -  For cohort 2: intermediate-2 or high risk MF patients as defined by DIPSS either not
             eligible for ruxolitinib or having failed under ruxolitinib

          -  No prior treatment for myelofibrosis (for cohort 1 only)

          -  Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0, 1 or 2

          -  Platelet count >= 100,000/mm^3 (obtained =< 14 days prior to registration)

          -  Absolute neutrophil count (ANC) >= 1000/mm^3 (obtained =< 14 days prior to
             registration)

          -  Aspartate transaminase (AST) =< 2.5 x upper limit of normal (ULN) (obtained =< 14 days
             prior to registration)

          -  Alanine aminotransferase (ALT) =< 2.5 x ULN (obtained =< 14 days prior to
             registration)

          -  Calculated creatinine clearance must be >= 50 ml/min using the Cockcroft-Gault formula
             (obtained =< 14 days prior to registration)

          -  Negative pregnancy test done =< 7 days prior to registration, for women of
             childbearing potential only

          -  Ability to complete questionnaire(s) by themselves or with assistance

          -  Provide informed written consent

          -  Willing to return to enrolling institution for follow-up

          -  Willing to provide blood samples for correlative research purposes

        Exclusion Criteria:

          -  Patients who have had chemotherapy or radiation =< 2 weeks of registration

          -  For cohort 1 only: patients with evidence of intermediate 2 or high risk disease
             (according to DIPSS)

          -  For cohort 1 only: patients with a bone marrow biopsy with < 15% cellularity, evidence
             of collagen fibrosis, osteosclerosis, or blasts > 10% in peripheral blood or marrow
             (demonstrating advanced disease)

          -  Patients who have received a prior stem cell transplant

          -  Patients who have received radiation to the spleen within 3 months prior to
             registration

          -  Patients with intolerance to compounds similar to pegylated interferon alpha-2b

          -  Patients with evidence of >= grade 2 peripheral sensory neuropathy

          -  Any of the following:

               -  Pregnant women

               -  Nursing women

               -  Men or women of childbearing potential who are unwilling to employ adequate
                  contraception

          -  Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment
             of the investigator, would make the patient inappropriate for entry into this study or
             interfere significantly with the proper assessment of safety and toxicity of the
             prescribed regimens

          -  Immunocompromised patients or patients known to be human immunodeficiency virus (HIV)
             positive and currently receiving antiretroviral therapy

          -  Uncontrolled simultaneous illness including, but not limited to, ongoing or active
             infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac
             arrhythmia, history of depression, or psychiatric illness/social situations that would
             limit compliance with study requirements

          -  Receiving any other investigational agent which would be considered as a treatment for
             the primary neoplasm

          -  History of myocardial infarction =< 6 months prior to registration, or congestive
             heart failure requiring use of ongoing maintenance therapy for life-threatening
             ventricular arrhythmias

          -  History of significant or major funduscopic findings including, but not limited to,
             retinal exudates, hemorrhage, detachment, neovascularization, papilledema, optic
             atrophy, micro-aneurysm or macular changes

          -  Other active malignancy at time of registration; EXCEPTIONS: non-melanotic skin cancer
             or carcinoma-in-situ of the cervix