A Phase I/II Trial to Evaluate a Peptide Vaccine Plus Ipilimumab in Patients With Melanoma

Inclusion Criteria: * Participants with stage IIA (with class 2 DecisionDx Score) through IV melanoma in cohorts defined below. These participants may have had cutaneous, uveal, mucosal primary melanoma, or an unknown primary melanoma. The diagnosis of melanoma must be confirmed by cytological or histological examination. Staging of cutaneous melanoma will be based on the revised AJCC staging system. Participants must be eligible to be treated with ipilimumab based on clinician judgment within standard of care. * Cohort 1 (Advanced Patients): unresectable stage III or IV melanoma that have clinical or radiographic evidence of disease. * Cohort 2 (Neoadjuvant therapy): primary melanoma with clinically apparent lymph node or in transit/satellite lesions with or without lymph node involvement, in transit recurrence or metastatic recurrence amenable to complete resection to no evidence of disease * Cohort 3 (Adjuvant therapy): Stage IIA (with class 2 DecisionDx Score), IIB-IV melanoma resected to no evidence of disease. * Participants will be required to have radiological studies to define radiologically evident disease. Required studies include: * Chest CT scan, * Abdominal and pelvic CT scan, and * Head CT scan or MRI PET/CT fusion scan may replace scans of the chest, abdomen, and pelvis. * Participants who have melanoma available for biopsy pre-treatment and on day 22 must consent to having those biopsies. Melanoma lesions may be in nodes, skin, soft tissue, liver, or other sites that can be accessed by core needle biopsy, or incisional or excisional biopsy, with or without image guidance. * Participants who have had brain metastases will be eligible if all of the following are true: * Each brain metastasis must have been treated by surgical removal, stereotactic radiosurgery or managed to complete resolution with immunotherapy. Patients with brain lesions managed by immunotherapy without excision or radiosurgery are included provided that the brain metastases have completely resolved after systemic therapy and there are no neurologic symptoms or need for systemic therapy to control CNS-disease related symptoms. * There has been no evident growth of any brain metastasis since the most recent treatment. If a patient has been managed by immunotherapy alone, the prior lesions must be completely resolved. * No brain metastasis is \> 2 cm in diameter at the time of registration * The most recent surgical resections or gamma-knife therapy for malignant melanoma must have been completed ≥ 1 week prior to registration. * ECOG performance status of 0 or 1 * Ability and willingness to give informed consent * Adequate lab function tests Age 18 years or older at registration. * Participants must have at least two intact (undissected) axillary and/or inguinal lymph node basins Exclusion Criteria: * Participants who have received the following medications or treatments at any time within 4 weeks of registration: * Chemotherapy * Interferon (e.g. Intron-A®) * Radiation therapy (Stereotactic radiotherapy, such as gamma knife, can be used ≥ 1 week prior to registration) * Allergy desensitization injections * High doses of systemic corticosteroids, with the following qualifications and exceptions: * Daily doses of 10 mg predisone (or equivalent) per day administered parenterally or orally are not allowed in patients with normal adrenal and pituitary function. * In patients with adrenal or pituitary insufficiency replacement steroid doses are allowed. * Inhaled steroids (e.g.: Advair®, Flovent®, Azmacort®) are permitted at low doses (less than 500 mcg fluticasone per day, or equivalent). * Topical and nasal corticosteroids are acceptable. * Growth factors (e.g. Procrit®, Aranesp®, Neulasta®) * Interleukins (e.g. Proleukin®) * Any investigational medication * Targeted therapies specific for mutated BRAF or for MEK * HIV positivity or evidence of active Hepatitis C virus (testing to be done within 6 months of study entry). * Participants who are currently receiving nitrosoureas or who have received this therapy within the preceding 6 weeks * Participants who are currently receiving a checkpoint molecule blockade therapy, or who have received this therapy within the preceding 6 weeks, with the following exceptions: * Participants who have received a PD-1 blocking antibody (eg: pembrolizumab or nivolumab) may be enrolled 3 weeks after receiving the last dose of that antibody. * Participants who have been treated previously with a CTLA-4 blocking antibody either as monotherapy or as part of combination CTLA-4/PD-1 blockade will be ineligible if CTLA-4 therapy: 1. was discontinued early for toxicity, or 2. did not induce stable disease or objective clinical response (by RECIST or irRC criteria) lasting 6 months or more. Note: Patients may be eligible if they have experienced progression after a period of stable disease (6 months or more) or an objective clinical response (by irRC or RECIST) (6 months or more) induced by CTLA-4 blockade or combination CTLA-4/PD-1 blockade. Note: Similar guidelines will apply for tremelimumab or other CTLA-4 blocking antibodies. * Participants with known or suspected allergies to any component of the vaccine. * Participants may not have been vaccinated previously with any of the synthetic peptides included in this protocol. Participants who have received vaccinations containing agents other than the synthetic peptides included in this protocol and have recurred during or after administration of the vaccine will be eligible to enroll 12 weeks following their last vaccination. * Pregnancy. * Female participants must not be breastfeeding * Participants in whom there is a medical contraindication or potential problem in complying with the requirements of the protocol in the opinion of the investigator. * Participants classified according to the New York Heart Association classification as having Class III or IV heart disease. Participants with uncontrolled diabetes, defined as having a HGB-A1C\> 7.5%. * Participants must not have had prior autoimmune disorders requiring cytotoxic or immunosuppressive therapy, or autoimmune disorders with visceral involvement. Participants with an active autoimmune disorder requiring these therapies are also excluded. The following will not be exclusionary: * The presence of laboratory evidence of autoimmune disease (e.g. positive ANA titer) without symptoms * Clinical evidence of vitiligo * Other forms of depigmenting illness * Mild arthritis requiring NSAID medications * A history of immune-related adverse events with immune therapy, if they have resolved completely. * Participants who have another cancer diagnosis, except that the following diagnoses will be allowed: * squamous cell cancer of the skin without known metastasis * basal cell cancer of the skin without known metastasis * carcinoma in situ of the breast (DCIS or LCIS) * carcinoma in situ of the cervix * any cancer without distant metastasis that has been treated successfully, without evidence of recurrence or metastasis for over 2 years * Participants with known addiction to alcohol or drugs who are actively taking those agents, or participants with recent (within 1 year) or ongoing illicit IV drug use. * Body weight \< 110 pounds at registration, due to the amount and frequency with which blood will be drawn.