Neoantigen Vaccine Plus Locally Administered Ipilimumab and Systemic Nivolumab in Advanced Melanoma

Inclusion Criteria: * Participant is willing and able to give written informed consent * Participants must have histologically confirmed cutaneous melanoma that is unresectable stage III or stage IV; at least one site of disease must be resectable, partially-resectable, or amenable to core biopsies to provide tumor tissue for sequence analysis. Participants with mucosal or uveal melanoma are excluded. * Participants must have measurable disease by RECIST v1.1 that has not been treated with local therapy within the last 12 months of study treatment. The measurable lesion and the lesion used for surgical or core biopsies can be identical as long as it remains measurable after biopsy * Age ≥ 18 years * ECOG performance status of 0 or 1 * Recovered from all toxicities associated with prior treatment, to acceptable baseline status (as to Lab toxicity see below limits for inclusion) or a National Cancer Institute Common Terminology Criteria for Adverse Events (NCI CTCAE) version 4, Grade of 0 or 1, except for toxicities not considered a safety risk, such as alopecia or vitiligo * Participants must have normal organ and marrow function as defined below: * WBC ≥3,000/µL * ANC ≥1,500/µL * Platelets ≥100,000/µL * Hemoglobin ˃ 9.0 g/dL * Total Bilirubin ≤ 1.5 x ULN (except subjects with Gilbert Syndrome, who can have total bilirubin \< 3.0 mg/dL) * AST(SGOT)/ALT(SGPT) ≤ 3 x ULN * Creatinine ≤ 1.5 x ULN OR * Creatinine clearance ≥40 mL/min/1.73 m2 for participants with creatinine levels above institutional normal (if using the Cockcroft-Gault formula below): * Female CrCl = (140 - age in years) x weight in kg x 0.85 72 x serum creatinine in mg/dL * Male CrCl = (140 - age in years) x weight in kg x 1.00 72 x serum creatinine in mg/dL * Women of childbearing potential (WOCBP) should have a negative serum pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 24 hours prior to the start of Nivolumab, because the effects of NeoVax plus Montanide and Nivolumab on the developing human fetus are unknown * Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with study agents, breastfeeding should be discontinued if the mother is treated with Ipilimumab, Nivolumab and Personalized Neoantigen vaccine + Montanide. * Female participants enrolled in the study, who are not free from menses for \>2 years, post hysterectomy / oophorectomy, or surgically sterilized, should be willing to use either 2 adequate barrier methods or a barrier method plus a hormonal method of contraception to prevent pregnancy or to abstain from sexual activity throughout the study, starting with visit 1 through 23 weeks (30 days plus the time required for Nivolumab to undergo five half-lives) after the last dose of study therapy. Approved contraceptive methods include for example: intra uterine device, diaphragm with spermicide, cervical cap with spermicide, male condoms, or female condom with spermicide. Spermicides alone are not an acceptable method of contraception. 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. * Male participants should agree to use an adequate method of contraception starting with visit 1 through 31 weeks after the last dose of study therapy * Eligibility Criteria for Secondary Registration * ECOG performance status of 0 or 1 * Screening laboratory values must meet the following criteria and should be obtained within 7 days prior to registration * WBC ≥ 3000/μL * Neutrophils ≥ 1500/μL * Platelets ≥ 100 x103/μL * Hemoglobin \> 9.0 g/dL * Serum creatinine ≤ 1.5 x ULN or creatinine clearance (CrCl) ≥ 40 mL/min (if using the Cockcroft-Gault formula below): * Female CrCl = (140 - age in years) x weight in kg x 0.85 72 x serum creatinine in mg/dL * Male CrCl = (140 - age in years) x weight in kg x 1.00 72 serum creatinine in mg/dL * AST/ALT ≤ 3 x ULN * Total Bilirubin ≤ 1.5 x ULN (except subjects with Gilbert Syndrome, who can have total bilirubin \< 3.0 mg/dL) * Women of childbearing potential (WOCBP) should have a negative serum pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 24 hours prior to the start of Nivolumab, because the effects of NeoVax plus Montanide and Nivolumab on the developing human fetus are unknown * Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with study agents, breastfeeding should be discontinued if the mother is treated with Ipilimumab, Nivolumab and Personalized Neoantigen vaccine + Montanide. * Female participants enrolled in the study, who are not free from menses for \>2 years, post hysterectomy / oophorectomy, or surgically sterilized, should be willing to use either 2 adequate barrier methods or a barrier method plus a hormonal method of contraception to prevent pregnancy or to abstain from sexual activity throughout the study, starting with visit 1 through 23 weeks (30 days plus the time required for Nivolumab to undergo five half-lives) after the last dose of study therapy. Approved contraceptive methods include for example: intra uterine device, diaphragm with spermicide, cervical cap with spermicide, male condoms, or female condom with spermicide. Spermicides alone are not an acceptable method of contraception * Male participants should agree to use an adequate method of contraception starting with visit 1 through 31 weeks after the last dose of study therapy Exclusion Criteria: * Prior immunotherapy for metastatic melanoma except anti-CTLA-4 * Concomitant therapy with any anti-cancer agents, other investigational anti-cancer therapies, or immunosuppressive agents including but not limited to methotrexate, chloroquine, azathioprine, etc. within six months of study participation * Active brain metastases or leptomeningeal metastases * Use of a non-oncology vaccine therapy for prevention of infectious diseases during the 4 week period prior to first dose of Nivolumab. Participants may not receive any non-oncology vaccine therapy during the period of Nivolumab or NeoVax plus Montanide administration and until at least 8 weeks after the last dose of study therapy * History of severe allergic reactions attributed to any vaccine therapy for the prevention of infectious diseases * Active, known or suspected autoimmune disease. Subjects are permitted to enroll if they have vitiligo, type I diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger * A condition requiring systemic treatment with either corticosteroids (\> 10 mg daily prednisone equivalents) or other immunosuppressive medications within 14 days of study drug administration. Inhaled or topical steroids and adrenal replacement doses \> 10 mg daily prednisone equivalents are permitted in the absence of active autoimmune disease * test positive for hepatitis B virus surface antigen (HBV sAg) or hepatitis C virus ribonucleic acid (HCV antibody) indicating acute or chronic infection * Known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS) * Uncontrolled intercurrent illness including, but not limited to ongoing or active infection requiring treatment, symptomatic * Any underlying medical condition, psychiatric condition or social situation that in the opinion of the investigator would compromise study administration as per protocol or compromise the assessment of AEs * Planned major surgery * Pregnant women are excluded from this study because Nivolumab, personalized neoantigen peptides and poly-ICLC are agents with unknown risks to the developing fetus. Because there is an unknown but potential risk of adverse events in nursing infants secondary to treatment of the mother with Nivolumab, personalized neoantigen peptides and poly-ICLC, nursing women are excluded from this study * Individuals with a history of an invasive malignancy are ineligible except for the following circumstances: a) individuals with a history of invasive malignancy are eligible if they have been disease-free for at least 3 years and are deemed by the investigator to be at low risk for recurrence of that malignancy; b) individuals with the following cancers are eligible if diagnosed and treated - carcinoma in situ of the breast, oral cavity or cervix, localized prostate cancer, basal cell or squamous cell carcinoma of the skin