The main purpose of this study is to examine the safety and tolerability of CDX-1401 when given in combination with an immune stimulant (resiquimod) to patients with advanced cancers that are known to express the NY-ESO-1 protein.

NY-ESO-1 is a protein that is often made by some types of tumor cells, but only made by a few types of normal cells. Because it is primarily made by cancer cells, the NY-ESO-1 protein is a promising target against which to stimulate an immune response that may destroy cancer cells. CDX-1401 is a cancer vaccine that is specially designed to create this type of immune response. To enhance the immune response, CDX-1401 will be given with 1 or 2 immune stimulants called Resiquimod and poly-ICLC (Hiltonol).

This clinical trial includes Phase 1 and Phase 2 segments. During the Phase 1 segment, six groups of 6 to 24 patients will be treated with different dose levels of CDX-1401 in combination with either one or both of the immune stimulants (Resiquimod and/or poly-ICLC). This phase of the study will test the safety profile of the vaccine treatment, and will assess which dose to test in future studies. During the Phase 2 segment, 14 patients whose cancer tested positive for the NY-ESO-1 protein in laboratory testing, will receive the study treatment to determine if it has an effect on their cancer. All patients enrolled in either part of the study may continue to receive study treatment until their disease has progressed or until it is necessary to stop the treatment for safety or other reasons. In addition, all patients will be "followed" for 24 months after enrollment in order to collect survival information.

Inclusion Criteria:

Among other criteria, patients must meet all of the following conditions to be eligible to be in the study:

1. 18 years of age or older.
2. Have a cancer type that is known to express NY-ESO-1, including (but not limited to) cancer of the bladder, breast, ovary, non-small cell lung cancer, myeloma, sarcoma or melanoma.
3. Have cancer that has progressed after any therapies with curative potential or approved salvage therapies (if such therapies exist).
4. Have evaluable or measurable tumors.
5. Have adequate blood, bone marrow, liver and kidney function as determined by laboratory tests.
6. Have a sample of tumor tissue available for NY-ESO-1 testing at a central laboratory.
7. If of childbearing potential (male or female), agree to practice an effective form of contraception during study treatment.

Exclusion Criteria:

Among other criteria, patients who meet any of the following conditions are NOT eligible to be in the study:

1. Are receiving treatment with immunosuppressive or immunomodulatory agents, including any systemic steroid (inhaled or topically applied steroids are permitted).
2. Has a known infection with HIV, HBV or HCV, or any other active infection requiring systemic antibiotic treatment.
3. Has active central nervous system tumors.
4. Any underlying medical condition that in the Principal Investigator's opinion will make the administration of study drug hazardous or otherwise interfere with the study.