Inclusion Criteria:

          -  Adults with JAK2 V617F+ primary myelofibrosis (PMF) or post-polycythemia vera
             (PV)/essential thrombocythemia myelofibrosis (ET-MF) who require treatment and have
             intermediate or higher risk disease (as assessed by the International Prognostic
             Scoring System for Myelodysplastic Syndrome [IPSS], Dynamic International Prognostic
             Scoring System [DIPSS], DIPSS-plus, Mutation-Enhanced Prognostic System for Transplant
             Age Patients with Primary Myelofibrosis [MIPSS70], MIPSS70-plus version [v] 2.0, or
             MYelofibrosis SECondary to PV and ET-Prognostic Model [MYSEC-PM]). The MYSEC-PM is to
             only be used for patients with post-PV/ET MF

          -  Patients must not be candidates for JAK inhibitor therapy in the opinion of the
             treating physician

          -  Bone marrow (BM) fibrosis grade 2 or 3 according to the European classification

          -  Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1 or 2 (Karnofsky
             performance status >= 60%)

          -  Absolute neutrophil count >= 0.5 x 10^9/L

          -  Direct bilirubin =< 1.5 x institutional upper limit of normal

          -  Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase
             [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT])
             =< 2.5 x institutional upper limit of normal unless felt to be due to liver
             involvement by MF/extramedullary hematopoiesis, in which case =< 5 x institutional
             upper limit of normal is permissible

          -  Creatinine =< 2 x institutional upper limit of normal OR creatinine clearance >= 30
             mL/min/1.73 m^2 for patients with creatinine levels above institutional normal

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

          -  Women of child-bearing potential and men must agree to use adequate contraception
             (hormonal or barrier method of birth control; abstinence) prior to study entry and for
             the duration of study participation until 6 months after the last administration of
             elotuzumab. Should a woman become pregnant or suspect she is pregnant while she or her
             partner is participating in this study, she should inform her treating physician
             immediately. Women of child-bearing potential must have a negative pregnancy test. Men
             treated or enrolled on this protocol must also agree to use adequate contraception
             prior to the study, for the duration of study participation, and 6 months after the
             last administration of elotuzumab

        Exclusion Criteria:

          -  Splenic irradiation within the preceding 4 months

          -  Chemotherapy (other than hydroxyurea), interferons, IMiDs, danazol or other androgens,
             erythroid stimulating agents, or other MF-directed commercially available agents
             within 4 weeks prior to entering the study or those who have not recovered to baseline
             from adverse events due to agents administered more than 4 weeks earlier

          -  Other investigational agents within 4 half-lives prior to study entry

          -  History of allergic reactions attributed to compounds of similar chemical or biologic
             composition to elotuzumab

          -  Patients with known central nervous system (CNS) involvement

          -  Prior allogeneic hematopoietic cell transplantation (allo-HCT) for MF

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

          -  Known pregnancy or lactation

          -  Known human immunodeficiency virus (HIV), hepatitis B virus (HBV) or hepatitis C virus
             (HCV) positivity