Study to Assess Safety and Immune Response of Stage IIB-IV Resected Melanoma After Treatment With MAGE-A3 ASCI

Inclusion Criteria: * Histologically or cytologically proven melanoma that meets one of the following two criteria: * Stage IIB-IV melanoma rendered clinically free of disease by surgery, other therapy, or spontaneous remission within 6 months prior to registration. * Stage III or IV melanoma with disease. Patients may be eligible if there are definite or equivocal findings of persistent or metastatic disease as long as those findings do not meet RECIST criteria for measurable disease. * Expression of MAGE-A3 by the tumor (primary or metastasis). * Patients may have had multiple primary melanomas. * Patients may have had, or may have, a metastasis from a cutaneous, mucosal, unknown primary site. * Patients with brain metastases may be eligible if all of the following are true: * The total number of brain metastases ever is less than or equal to 3. * The brain metastases have been completely removed by surgery or have been treated completely by stereotactic radiotherapy. Stereotactic radiotherapy, such as gamma knife, can be used up to 1 week prior to study entry. * There has been no evident growth of any brain metastasis since treatment. * No treated brain metastasis is greater than 2 cm in diameter at the time of protocol entry. * Patients must have at least two intact axillary and/or inguinal lymph node basins. * The interferon education packet must be completed satisfactorily for those who are eligible for, but refuse, interferon therapy. * All patients must have: * ECOG performance status of 0 or 1. * Ability and willingness to give informed consent. * Laboratory parameters as follows: 1. ANC \> 1000/mm3, and Platelets \> 75,000/mm3 and Hgb \> 9 g/dL 2. Hepatic: AST and ALT up to 2.5 x upper limits of normal (ULN) Bilirubin up to 2.5 x ULN Alkaline phosphatase up to 2.5 x ULN LDH up to 2x ULN 3. Renal: Creatinine up to 1.5 x ULN 4. Serology: HIV negative (antibody screening), Hepatitis C negative 5. HGBA1C level of \< 7.5% * Patients must be 18 years or older at study entry Exclusion Criteria: * Patients with primary ocular melanoma. * Patients who have had brain metastases unless they meet the criteria outlined in the inclusion criteria * Patients who are currently receiving systemic cytotoxic chemotherapy, radiation, monoclonal antibody therapy, or other experimental therapy, or who have received this therapy within the preceding 4 weeks. Patients who are currently receiving nitrosoureas or who have received this therapy within the preceding 6 weeks. * Patients who have received isolated limb infusion (ILI) or isolated limb perfusion (ILP) for melanoma will not be eligible unless they have experienced tumor progression after the ILI/ILP, and the ILI/ILP was not performed within the prior 12 weeks. * Patients will not be eligible if there is clinically detectable melanoma deemed likely by the investigator to require intervention during the first 12 weeks of the study that would require premature discontinuation. * Patients with known or suspected allergies to any component of the MAGE-A3 ASCI. * Patients receiving the following medications at study entry or within the preceding 4 weeks are excluded, except as specified below: 1. Agents with putative immunomodulating activity, but with the exception of non-steroidal anti-inflammatory agents and topical steroids. 2. Antibodies to CTLA-4, PD-1, PD-L1, or CD137 may not have been received in the past 12 weeks, and patients will be eligible only if there has been melanoma progression since that therapy was administered. 3. Allergy desensitization injections. 4. Systemic corticosteroids, administered parenterally or orally. Inhaled steroids are not permitted. Topical corticosteroids are acceptable, including steroids with very low solubility administered nasally for local effects only. 5. Any growth factors (e.g. GM-CSF, G-CSF, erythropoietin). 6. Interferon therapy. 7. Interleukin-2 or other interleukins. 8. Targeted therapies designed to inhibit BRAF, MAPKinase, mTOR, or their signaling pathways. * Prior active immunotherapy or vaccines for melanoma may be an exclusion criterion in some circumstances. Exceptions to this exclusion criterion are as follows: 1. Patients who have recurred or progressed either after or during administration of a melanoma vaccine may be eligible to enroll in this study 12 weeks following their last vaccination. 2. Patients may not have been previously administered the synthetic MAGE-A3 protein, though prior vaccinations with up to 4 synthetic MAGE-A3 peptides (up to 16 amino acids in length, each) is allowed. * Pregnancy or the possibility of becoming pregnant during vaccine administration. Female patients of child-bearing potential must have a negative pregnancy test (urinary or serum beta-HCG) prior to administration of the first MAGE-A3 ASCI dose. Males and females must agree, in the consent form, to use effective birth control methods during the course of vaccination. Women must also not be breast feeding. This is consistent with existing standards of practice for vaccine and chemotherapy protocols. * Patients in whom there is a medical contraindication or potential problem in complying with the requirements of the protocol, in the opinion of the investigator. * Patients classified according to the New York Heart Association classification as having Class III or IV heart disease. * Patients with a body weight \< 110 lbs because of the amount and frequency with which blood will be drawn, and because of the biopsies required. * Patients must not have had prior autoimmune disorders requiring cytotoxic or immunosuppressive therapy, or autoimmune disorders with visceral involvement. Patients with an active autoimmune disorder requiring these therapies are also excluded. The following will not be exclusionary: * 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