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
