This study evaluates whether it is safe to administer a peptide vaccine made of 6MHP and a mutated neoantigen peptide (BRAF585-614-V600E) combined with adjuvants. The adjuvants that will be used in this trial are a CD40 antibody (CDX-1140) and a toll-like receptor (TLR) 3 agonist (Poly-ICLC). The study will also investigate the effects of the vaccine and the adjuvants on the immune response. The investigators will monitor these effects by performing tests in the laboratory on participants' blood and skin tissue.

Main Inclusion Criteria:

1. a. For individuals with primary cutaneous, mucosal, or unknown melanoma, an individual must have stage IB ulcerated, II, III, or IV melanoma at original diagnosis or at restaging after recurrence, and be rendered clinically free of disease by surgery, other therapy, or spontaneous remission within 6 months prior to registration.

   b. For patients with stage II, III, or IV uveal melanoma, patients must be rendered clinically free of disease by surgery, other therapy, or spontaneous remission within 6 months prior to registration.

2. An individual with small radiologic or clinical findings of an indeterminate nature may still be eligible

3. An individual may have had cutaneous, uveal, mucosal primary melanoma, or an unknown primary melanoma.

4. Biopsies of nevi are optional. Participants with at least 4-10 evaluable nevi at least 4 mm in diameter that are located on truncal or non-acral extremity sites and are accessible for biopsy and observation will be asked to participate in the optional nevi biopsies

5. Diagnosis of melanoma must be confirmed by cytological or histological examination except that patients with clinically localized primary uveal melanoma will not require pathologic review.

6. Individuals will be required to have radiological studies to rule out radiologically evident melanoma metastasis.

7. Individuals who have had brain metastases will be eligible if all of the following are true:

   • Each brain metastasis must have been completely removed by surgery or each unresected brain metastasis must have been treated with stereotactic radiosurgery.
   • No brain metastasis is > 2 cm in diameter at the time of registration.
   • Any neurologic symptoms attributable to brain metastases have returned to baseline.
   • There is no evidence of new or enlarging brain metastases.

8. The most recent surgical resections or gamma-knife therapy for malignant melanoma must have been completed ≥ 1 week and ≤ 6 months prior to registration.

9. ECOG performance status of 0 or 1 (Section 13.3).

10. Ability and willingness to give informed consent.

11. Adequate organ function as determined by laboratory parameters.

12. Male or female, age 18 years or older at registration.

13. Individuals must have at least one intact (undissected) axillary and/or inguinal lymph node basin.

14. For females and males of reproductive potential: agreement to use adequate contraception during study participation and for an additional 3 months after receiving the last dose of study drug.

Main Exclusion Criteria:

1. Individuals 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 and ≤ 6 months prior to registration)
   • Allergy desensitization injections
   • High doses of systemic corticosteroids, with some qualifications and exceptions
   • Growth factors (e.g. Procrit®, Aranesp®, Neulasta®)
   • Interleukins (e.g. Proleukin®)
   • Any investigational medication
   • Targeted therapies specific for mutated BRAF or for MEK

2. Individuals who are currently receiving nitrosoureas or who have received this therapy within 6 weeks of registration.

3. Individuals who are currently receiving a checkpoint molecule blockade therapy, or who have received this therapy within 12 weeks of registration.

4. Individuals with known or suspected allergies to any component of the vaccine.

5. Individuals who have received prior melanoma vaccinations with 6MHP plus the mutated BRAF peptide. However, participants who have received prior vaccinations will be eligible to enroll 12 weeks following their last vaccination if they have recurred during or after administration of the vaccine, and if their vaccines did not include all of the synthetic peptides included in this protocol.

6. Individuals who have previously received CDX-1140 or another CD40 agonistic antibody.

7. Pregnancy. Female individuals of childbearing potential must have a negative pregnancy test (urinary or serum beta-HCG) obtained within 2 weeks prior to registration.

8. HIV positivity or evidence of active Hepatitis C virus (testing to be done within 6 months of study entry).

9. Female individuals must not be breastfeeding.

10. Individuals in whom there is a medical contraindication or potential problem in complying with the requirements of the protocol in the opinion of the investigator.

11. Individuals classified according to the New York Heart Association classification as having Class III or IV heart disease (Section 13.4).

12. Individuals must not have had prior autoimmune disorders requiring systemic cytotoxic or immunosuppressive therapy, or autoimmune disorders with visceral involvement. Participants with an active autoimmune disorder requiring these therapies are also excluded. Some autoimmune disorders 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 non-steroidal anti-inflammatory drugs (NSAID) medications
    • Resolved childhood asthma/atopy
    • Endocrinopathies on stable hormone replacement therapy

13. Individuals 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.

14. Individuals with current pneumonitis. Individuals must not have had pneumonitis within 30 days of registration. Patients who have had complete resolution of prior pneumonitis will be eligible.

15. Individuals who have received a live vaccine within 30 days of registration.

16. Body weight < 110 pounds (50 kg) at registration