Epacadostat and Vaccine Therapy in Treating Patients With Stage III-IV Melanoma

Inclusion Criteria: * Patients must have malignant melanoma validated by histology or cytology; patients may have had primary cutaneous, mucosal, or ocular melanoma or metastasis from an unknown primary site * NOTE: patients must have measurable disease, defined as at least 1 lesion that can be accurately measured in at least 1 dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as \>= 20 mm with conventional chest x-ray or as \>= 10 mm with spiral computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam * Unresectable stage III or IV validated by clinical criteria (including recurrent melanoma), or patients with multiple skin/soft tissue metastases of melanoma that may be resectable but are judged to have a future recurrence risk exceeding 70% (e.g., large adenopathy, distant skin metastases or multiple in-transit melanoma metastases); tumor deemed amenable to biopsy (excisional, incisional, or core, with at least 100 mm\^3 tumor volume per biopsy date) and fine-needle aspiration (FNA) biopsy * NOTE: optimally, patients will have tumor approachable for three serial biopsies during the trial; for patients with only one or two tumors approachable for biopsy, available tumor blocks from prior biopsies can serve as the pretreatment sample, but only if formalin-fixed tumor tissue is available and adequate to provide at least 20 unstained slides with sufficient tumor for analysis * NOTE: patients with unresectable advanced stage III or IV melanoma (including recurrent melanoma) are only eligible if they have failed at least one other first-line systemic therapy (other than adjuvant therapy); exceptions to this requirement are those patients who have refused and/or are ineligible for other systemic therapies * NOTE: v-raf murine sarcoma viral oncogene homolog B inhibitor (BRAFi) should be considered for all 'unresectable" or metastatic melanoma with BRAFV600E mutation; for low burden in-transit disease patients may enter trial without prior systemic therapy * Stage IV no evidence of disease (NED) is excluded by this criterion * Patients may have had prior systemic therapy without constraint on the number of prior treatment regimens except: * Patients may not have had \> 450 mg/m\^2 doxorubicin * Patients may not have had \> 3000 centigray (cGy) to fields encompassing the entire pelvis * Patients must not be on any other systemic therapy within the following intervals before study enrollment: * 1 week after stereotactic radiosurgery of the brain or comparable technology * 4 weeks after cytotoxic chemotherapy or external beam radiation therapy * 6 weeks after chemotherapy regimens including BCNU (carmustine) or mitomycin C * Patients who experience melanoma progression (by Response Evaluation Criteria in Solid Tumors \[RECIST\] 1.1 criteria) while on or after treatment with programmed cell death 1 (PD-1) or PD ligand-1 (PDL-1) antibody may enroll on this study * NOTE: Patients must be off PD-1/PDL- antibody for at least 2 weeks to assess for delayed toxicity before being enrolled and receiving INCB024360; patients who are enrolled 2 weeks and up to 6 weeks after the last dose of PD-/PDL-1 antibody will enroll in cohort B and receive 100 mg BID of INCB024360; patients enrolled beyond the 6 week period after failing anti-PD-1/PDL-1 will be enrolled in cohort A; cohort A patients will receive 300 mg BID of INCB024360; patients must not have active grade 2 autoimmune toxicities attributed to these antibodies at study entry * 8 weeks after ipilimumab, other cytotoxic T-lymphocyte-associated protein 4 (CTLA-4) antibody or other immunologically active antibody * NOTE: Patients receiving prior CTLA-4, anti-PD1 antibody or other immunologic therapy must show evidence of normal pituitary function at baseline and must not have active grade 2 autoimmune toxicities attributed to these antibodies at study entry * Eastern Cooperative Oncology Group (ECOG) performance status 0-1 (Karnofsky \>= 70%) * Life expectancy of at least 6 months * Leukocytes \>= 3,000/mcL * Absolute neutrophil count \>= 1,500/mcL * Platelets \>= 75,000/mcL * Hemoglobin \> 9 g/dL * Total bilirubin \< 1.5 x institutional upper limit of normal (bilirubin \< 3 × institutional upper limit of normal for Gilbert's syndrome) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) up to 2.5 times upper limit normal (ULN) * Creatinine \< 1.5 x institutional upper limit of normal OR * Creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * Prothrombin time (PT), international normalized ratio (INR) =\< 1.5 x institutional ULN unless patient is therapeutically anticoagulated; if on anticoagulants, PT/INR need to be within appropriate anticoagulation limits for the clinical indication; patients who are receiving anticoagulants may participate in the trial if their anticoagulation can be stopped safely for several days at the time of each biopsy * Thyroid-stimulating hormone (TSH) up to 4 times ULN if thyroxine (T4) is normal * T4 within normal limits; if abnormal and patient is receiving thyroid replacement therapy, the thyroid medication may be adjusted and the T4 may be re-tested * Patients must express human leukocyte antigen (HLA) -A1+, -A2+, or -A3+ (80% of patients) * Lactate dehydrogenase (LDH) \< 5 × upper limits of normal * (NOTE: these criteria will select against patients with bulky disease and will select for patients with less disease and earlier disease) * Participants must not have had prior autoimmune disorders requiring cytotoxic or immunosuppressive therapy, or autoimmune disorders with visceral involvement; participants must not have an active or inactive autoimmune disorders (e.g., rheumatoid arthritis, moderate or severe psoriasis, multiple sclerosis, inflammatory bowel disease, etc.); participants who are receiving therapy for an autoimmune or inflammatory disease requiring these therapies are also excluded * The following will not be exclusionary: * Resolved ipilimumab associated inflammatory disease * The presence of laboratory evidence of autoimmune disease (e.g., positive antinuclear antibody \[ANA\] titer) without associated symptoms * Subjects with vitiligo, thyroiditis, or atopic dermatitis, but otherwise not meeting this criterion may be enrolled; individual cases can be discussed with the sponsor * Not likely curable with surgery alone * Not currently receiving therapy * Females of childbearing potential must have a negative pregnancy test within 48 hours before initiating protocol therapy * NOTE: women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control or abstinence) before study entry and for the duration of study participation; 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; men treated or enrolled on this protocol must also agree to use adequate contraception before the study, for the duration of study participation, and 4 months after completing INCB024360 and MELITAC 12.1 administration * NOTE: subjects are considered not of child bearing potential if they are surgically sterile, have undergone a hysterectomy, bilateral tubal ligation, or bilateral oophorectomy, or are postmenopausal; menopause is the age associated with complete cessation of menstrual cycles and menses, and implies the loss of reproductive potential; by a practical definition, the term assumes menopause after 1 year without menses with an appropriate clinical profile at the appropriate age * Ability to understand and willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had cytotoxic chemotherapy, radiotherapy, interferon (IFN), immunosuppressive therapy, or steroids within 4 weeks (6 weeks for nitrosoureas or mitomycin C) before entering the study or those who have not recovered from adverse events (AEs) due to agents administered more than 4 weeks earlier * Ipilimumab or other immunologically active therapy within 8 weeks of enrollment; NOTE: patients who experience melanoma progression (by RECIST 1.1 criteria) while on or after treatment with PD-1 or PDL-1 antibody may enroll on this study * Active immunosuppressive therapy, including concurrent systemic immunosuppressive therapy or steroid therapy with more than 7 consecutive days of steroids within the prior 4 weeks * The use of prednisone or equivalent \< 0.125 mg/kg/day (absolute maximum of 10 mg/day) as replacement therapy is permitted * Inhaled corticosteroids are permitted * Cardiovascular disease that meets one of the following: congestive heart failure (New York Heart Association class III or IV), active angina pectoris, or recent myocardial infarction or acute coronary syndrome (within the last 6 months) * History of peripheral vascular disease (PVD) that has required surgical or percutaneous intervention or documented PVD that requires medical management with medications such as acetylsalicylic acid (ASA) + clopidogrel; patients with diabetes that is not well controlled are excluded from participation; not well controlled is defined as a hemoglobin (Hgb) A1C of greater than 7.5% * Current or history of systemic autoimmune disease requiring systemic therapy, including significant autoimmunity associated with prior ipilimumab therapy or therapy with antibodies to PD-1 or PD-L1 * Cirrhosis, chronic hepatitis C virus positivity, or chronic hepatitis B infection; subjects who may not tolerate immune-mediated hepatitis due to compromised hepatic reserve also excluded from participation including: subjects with extensive liver metastasis (as judged by the investigator); subjects who drink more than two standard alcoholic beverages per day on a regular basis; subjects who consume more than 2 grams of acetaminophen per day on a regular basis * A positive hepatitis B serology indicative of previous immunization (i.e., hepatitis B surface antibody \[HBsAb\]-positive and hepatitis B core antibody \[HBcAb\]-negative), or a fully resolved acute hepatitis B infection is not an exclusion criterion * Patients who are receiving any other investigational agents for melanoma * Patients who have had a grade one or grade two gastrointestinal adverse event during or after receiving anti-CTLA-4, anti-PD1 or anti-PD, without a colonoscopy verifying complete resolution of the adverse event * Patients who have experienced bowel perforation, neurologic involvement, Guillain Barré syndrome, Myasthenia Gravis, Steven Johnson syndrome and other intractable events or grade 4 non-laboratory toxicity * 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 * Pregnancy, nursing, or unwilling to take adequate birth control during therapy * NOTE: pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with INCB024360 and MELITAC 12.1 * Known human immunodeficiency virus (HIV) or other history of immunodeficiency disorder * NOTE: HIV-positive patients taking combination antiretroviral therapy are ineligible * Extensive active brain disease, including symptomatic brain metastases or the presence of leptomeningeal disease * Patients with brain metastasis, after definitive therapy with surgery or stereotactic radiation and stable off steroids for \> 4 weeks, are eligible * Any malignancy that has not been in complete remission for at least 3 years * NOTE: patients with cured basal or squamous cell skin cancer are not excluded; patients with a history of excised in situ cancers, including breast, cervical, colon, superficial bladder, prostate or other body system are not excluded; study entry will be allowed at the discretion of the Principal Investigator * NOTE: recurrence of the in situ cancer or tumor at the time of study entry would be exclusionary * Monoamine oxidase (MAO) inhibitor use within the past 3 weeks or prior evidence of serotonin syndrome * History of allergic reactions attributed to compounds of similar chemical or biologic composition to INCB024360, MELITAC 12.1, or other vaccine components * Prior organ allograft or allogeneic transplantation, if the transplanted tissue is still in place * Medical or psychiatric illness that would, in the opinion of the investigator, preclude participation in the study or the ability of patients to provide informed consent for themselves * History of pulmonary disease such as emphysema or chronic obstructive pulmonary disease (COPD), (forced expiratory volume in one second \[FEV1\] \> 60% of predicted for height and age); pulmonary function tests (PFTs) are required in patients with prolonged smoking history or symptoms of respiratory dysfunction * Use of any UDP glucuronosyltransferase 1 family, polypeptide A9 (UGT1A9) inhibitor including: acitretin, amitriptyline, androsterone, cyclosporine, dasatinib, diclofenac, diflunisal, efavirenz, erlotinib, estradiol (17-beta), flutamide, geftinib, gemfibrozil, glycyrrhetinic acid, glycyrrhizin, imatinib, imipramine, ketoconazole, lineoleic acid, mefenamic acid, mycophenolic acid, niflumic acid, nilotinib, phenobarbital, phenylbutazone, phenytoin, probenecid propofol, quinidine, ritonavir, Sorafenib, sulfinpyrazone, valproic acid and verapamil from screening through follow-up period * Low-dose Coumadin (1 mg) is acceptable; however, doses that increase INR are not permitted; if an alternative to Coumadin-based anticoagulants cannot be used, the INR should be monitored weekly after initiation of therapy and upon discontinuation of INCB024360, until INR normalization