A Trial of CDX-1401 in Combination With Poly-ICLC and Pembrolizumab, in Previously Treated Advanced Solid Tumor Patients

Inclusion Criteria: * Be willing and able to provide written informed consent/assent for the trial. * Patients with previously treated advanced lung cancer (NSCLC, SCLC and mesothelioma), advanced triple negative breast cancer, urothelial cancers and malignant melanoma. Tumors should be positive for expression of NY-ESO-1, as assessed by external central laboratory testing. * Malignancy that has progressed after any therapies with curative potential or at least one approved palliative therapy for which the patient is a candidate. Patients with metastatic melanoma may be enrolled without prior treatment provided they meet rest of the eligibility criteria. * Where applicable, chemotherapy or radiation therapy must have been completed at least 4 weeks prior to the first dose of study treatment; the interval for prior anticancer therapeutic radiopharmaceuticals is at least 8 weeks. For patients on small molecule tyrosine kinase inhibitors therapy must have been completed 14 days prior to start of study treatment. The patient must have adequately recovered from any clinically significant toxicity experienced during prior treatment(s) in the investigator's opinion. * Chemoembolization, surgery or any other local therapy completed at least 4 weeks prior to the first dose of study treatment. * Have measurable disease based on immune-related Response Criteria (irRC). * Availability of tumor tissue (preferably from a recent biopsy or resection, or if not available, on the archived tumor tissue from the primary resection) for NY-ESO-1 expression analysis. Positive NY-ESO-1 expression will be required for entry. NY-ESO-1 expression will be analyzed at a central laboratory. * Have a performance status of 0 or 1 on the ECOG Performance Scale. * 10\. Demonstrate adequate organ function as defined below , all screening labs should be performed within 10 days of treatment initiation. * Absolute neutrophil count (ANC) \>=1,500/mcL * Platelets \>= 100,00/mcL * Hemoglobin \>= 9g/dL or \>= 5.6mmol/L without transfusion or EPO dependency (within 7 days of assessment) * Serum creatinine =\< 1.5X upper limit of normal * Measured creatinine clearance \>=mL/min for subject with creatinine levels \>1.5 X institutional upper limit of normal * Serum total bilirubin =\< 1.5X upper limit of normal * AST (SGOT) =\< 2.5 X upper limit of normal or =\< 5X upper limit of normal for subjects with liver metastases * ALT (SGPT) =\< 2.5 X upper limit of normal or =\< 5X upper limit of normal for subjects with liver metastases * Albumin \>= 2.5mg/dL * International Normalized Ratio =\< 1.5 X upper limit of normal unless subject is receiving anticoagulant therapy as long as Prothrombin Time or Partial Thromboplastin Time is within therapeutic range of intended use of anticoagulants Activated Partial Thromboplastin Time (aPTT) =\< 1.5 X upper limit of normal unless subject is receiving anticoagulant therapy as long as Prothrombin Time or Partial Thromboplastin Time is within therapeutic range of intended use of anticoagulants * Female subject of childbearing potential should have a negative urine or serum pregnancy within 72 hours prior to receiving the first dose of study medication. If the urine test is positive or cannot be confirmed as negative, a serum pregnancy test will be required * Female subjects of childbearing potential must be willing to use an adequate method of contraception - Contraception, for the course of the study through 120 days after the last dose of study medication. * Male subjects of childbearing potential must agree to use an adequate method of contraception - Contraception, starting with the first dose of study therapy through 120 days after the last dose of study therapy. Exclusion Criteria: * Is currently participating and receiving study therapy or has participated in a study of an investigational agent and received study therapy or used an investigational device within 4 weeks of the first dose of treatment. * Has a diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within 7 days prior to the first dose of trial treatment * Has a known history of active bacillus tuberculosis * Hypersensitivity to Pembrolizumab or any of its excipients * Has had a prior anti-cancer monoclonal antibody within 4 weeks prior to study day 1 or who has not recovered (ie =\< Grade 1 or at baseline) from adverse events due to agents administered more than 4 weeks earlier. * Has had prior chemotherapy, targeted small molecule therapy, or radiation therapy within 2 weeks prior to study Day 1 or who has not recovered (ie =\< Grade 1 or at baseline) from adverse events due to a previously administered agent. * Has a known additional malignancy that is progressing or required active treatment. Exceptions include basal cell carcinoma of the skin or squamous cell carcinoma of the skin that has undergone potentially curative therapy or in situ cervical cancer. * Has known active central nervous system metastases and/or carcinomatous meningitis. Subjects with previously treated brain metastases may participate provided therapy are stable (without evidence of progression by imagining for at least four weeks prior to the first dose of trial treatment and any neurologic symptoms have returned to baseline), have no evidence of new or enlarging brain metastases, and are not using steroids for at least 7 days prior to trial treatment. This exception does not include carcinomatous meningitis which is excluded regardless of clinical stability. * Has active autoimmune disease that has required systemic treatment in the past 2 years (ie with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (eg thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc) is not considered a form of systemic treatment. * Has known history of, or any evidence of active, non-infectious pneumonitis. * Has an active infection requiring systemic therapy. * Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the trial, interfere with the subject's participation for the full duration of the trial, or is not the best interest of the subject to participate, in the opinion of the treating investigator. * Is pregnant or breastfeeding, or expecting to conceive or father children within the projected duration of the trial, starting with the pre-screening or screening visit through 120 days after the last dose of trial treatment. * Has received prior therapy with an anti-PD-1, anti-PD-L1, anti-PD-L2 agent and previous administration of vaccine therapy targeting NY-ESO-1. * Has a known history of Human Immunodeficiency Virus (HIV) (HIV 1/2 antibodies). * Has known active Hepatitis B (e.g., HBsAg reactive) or Hepatitis C (e.g., HCV RNA \[qualitative\] is detected). * Has received a live vaccine within 30 days of planned start of study therapy. -- Note: seasonal influenza vaccines for injection are generally inactivated flu vaccines and are allowed; however intranasal influenza vaccines are live attenuated vaccines, and are not allowed.