Ability of a Dendritic Cell Vaccine to Immunize Melanoma or Epithelial Cancer Patients Against Defined Mutated Neoantigens Expressed by the Autologous Cancer

* INCLUSION CRITERIA:
* Metastatic melanoma or epithelial cancer with at least one lesion that is resectable or in selected cases, available peripheral blood mononuclear cells (PBMCs)
* Measurable and evaluable metastatic disease per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria
* Confirmation of the diagnosis of metastatic cancer by the Laboratory of Pathology of National Cancer Institute (NCI).
* All patients must be refractory to approved standard systemic therapy.
* Patients with 3 or fewer brain metastases that are less than 1 cm in diameter and asymptomatic are eligible. Lesions that have been treated with stereotactic radiosurgery must be clinically stable for one month after treatment for the patient to be eligible. Patients with surgically resected brain metastases are eligible.
* Greater than or equal to 18 years of age and less than or equal to 70 years of age.
* Clinical performance status of Eastern Cooperative Oncology Group (ECOG) 0, 1, 2
* Patients of both genders must be willing to practice birth control from the time of enrollment on this study and for up to four months after treatment.
* Serology:

  * Seronegative for Human Immunodeficiency Virus (HIV) antibody. (The experimental treatment being evaluated in this protocol depends on an intact immune system. Patients who are HIV seropositive can have decreased immune-competence and thus are less responsive to the experimental treatment and more susceptible to its toxicities.)
  * Seronegative for hepatitis B antigen, and seronegative for hepatitis C antibody. If hepatitis C antibody test is positive, then the patient must be tested for the presence of antigen by reverse transcriptase polymerase chain reaction (RT-PCR) and be hepatitis C virus ribonucleic acid (HCV RNA) negative.
* Hematology

  * Absolute neutrophil count greater than 1000/mm\^3 without the support of filgrastim
  * White blood cell (WBC) greater than or equal to 3000/mm\^3
  * Platelet count greater than or equal to 100,000/mm\^3
  * Hemoglobin \> 8.0 g/dl. Subjects may be transfused to reach this cut-off.
  * Cluster of differentiation 4 (CD4) count \> 200/uL
* Chemistry:

  * Serum alanine aminotransferase (ALT)/aspartate aminotransferase (AST) less than 5.0 x ULN
  * Serum Creatinine less than or equal to 1.6 mg/dl
  * Total bilirubin less than or equal to 2.0 mg/dl, except in patients with Gilbert's Syndrome, who must have a total bilirubin less than or equal to 3.0 mg/dl.
* More than four weeks must have elapsed since any prior systemic therapy at the time the patient receives the vaccine, and patients toxicities must have recovered to a grade 1 or less (except for toxicities such as alopecia or vitiligo).

Note: Patients may have undergone minor surgical procedures within the past 3 weeks, as long as all toxicities have recovered to grade 1 or less.

* Ability of subject to understand and the willingness to sign a written informed consent document.
* Subjects must be co-enrolled On protocol 03-C-0277.

EXCLUSION CRITERIA:

* Women of child-bearing potential who are pregnant or breastfeeding because of the potentially dangerous effects of the treatment on the fetus or infant.
* Any form of primary immunodeficiency (such as Severe Combined Immunodeficiency Disease).
* Concurrent opportunistic infections (The experimental treatment being evaluated in this protocol depends on an intact immune system. Patients who have decreased immune competence may be less responsive to the experimental treatment and more susceptible to its toxicities).
* Active systemic infections (requiring anti-infective treatment), coagulation disorders or any other active or uncompensated major medical illnesses.
* Patients who are receiving any other investigational agents.