Phase 1/2 With Expansion Cohorts in a Study of NEO-201 in Adults With Chemo-Resistant Solid Tumors

Inclusion Criteria: * Age: \>/=18 years * Diagnosis: * Subjects must have histologically or cytologically confirmed recurrent, locally advanced unresectable or metastatic cancer confirmed by the Laboratory of Pathology, NCI * Subjects enrolled in the expansion cohorts must have advanced non-small cell lung cancer, HNSCC, uterine cancer, or cervical cancer that has progressed during or after at least one front-line standard of care treatment, including chemotherapy and/or targeted therapy * Tumor is positive for NEO-201 antigen expression (defined as at least 10% of tumor cells expressing NEO-201 target antigen). * Patient is not a candidate for potentially curative surgery or radiation. Tumor has the additional characteristics described below for the disease specific expansion cohorts: NSCLC: * Tumor(s) must express PD-L1 (TSP \> 1%) as determined by an FDA-approved test and/or is microsatellite instability-high (MSI-H) or mismatch repair deficient, and/or is tumor mutational burden-high (TMB-H) \[≥10 mutations/megabase (mut/Mb)\], as determined by an FDA-approved test. * Patients with EGFR, ALK1, ROS1 or BRAF V600E genomic tumor aberrations must have had disease progression on FDA-approved agents for these aberrations. * Patients without these genomic tumor aberrations must have received immune-checkpoint inhibitor previously, either as a single agent or in combination with chemotherapy. Cervical Cancer: • Tumor(s) express a combined positive score (CPS) \> 1, as determined by an FDA approved test and/or is microsatellite instability-high (MSI-H) or mismatch repair deficient, and/or is tumor mutational burden-high (TMB-H) \[≥10 mutations/megabase (mut/Mb)\], as determined by an FDA-approved test HNSCC • Patients are allowed to have received pembrolizumab previously, either alone or as part of a multiagent regimen. Uterine carcinoma • Patients who are eligible to have received the combination of pembrolizumab plus lenvatinib (i.e. patients with tumors that are not MSI or dMMR) must have received this regimen, unless considered unsafe due to comorbid conditions (e.g. hypertension, proteinuria). * Must have archived tissue (10 unstained slides or tissue block), or must have tumor which can be safely biopsied percutaneously and be willing to undergo a tumor biopsy * MEASURABLE/EVALUABLE DISEASE: Measurable disease (by RECISTv1.1) * INFORMED CONSENT: Voluntary written informed consent before performance of any study-related procedure that is not part of normal medical care * PERFORMANCE STATUS: ECOG ≤ 2; or Karnofsky performance status of ≥ 50% * LABORATORY FUNCTION: * Screening laboratory data within 21 days of the first dose of study drug. Subject must have adequate organ function: * Hemoglobin \> 9 g/dL, or on stable doses (hematocrit stable within 1 gram and dose stable for one month) of erythropoietin or similar medication * Absolute neutrophil count (ANC) ≥1,500/mm3 * Platelets ≥ 100,000/mm3 * Total bilirubin ≤ 2.0 mg/dL * ALT and AST ≤ 3 times the ULN, or, if the subject has liver metastases, ≤ 5 times the ULN * Creatinine ≤ 1.5 mg/dL or creatinine clearance \> 40 mL/min/1.73 m2 for subjects with creatinine levels above institutional normal, as calculated by the Cockcroft Gault formula * PRIOR THERAPY: * At least 14 days must have elapsed since treatment with oral tyrosine kinase inhibitors, or until toxicities associated with TKI therapy have resolved * At least 21 days must have elapsed since treatment with previous monoclonal antibodies, or until toxicities associated with mAb therapy have resolved * At least 4 weeks must have elapsed since any chemotherapeutic agents at the time of enrollment (or 6 weeks for regimens containing BCNU or mitomycin C) * At least 2 weeks must have elapsed since any systemic corticosteroids at the time of enrollment * Immunotherapy: At least 42 days after the completion of any type of immunotherapy, e.g. tumor vaccines. * XRT: At least 7 days after local palliative XRT (small port) * Subjects must have recovered from any acute toxicity related to prior therapy, except for alopecia. Toxicity should be ≤ grade 1, or ≤ grade 2 for peripheral neuropathy, or hypothyroidism * Subject is expected to be able to remain on a study protocol for at least 8 weeks * BIRTH CONTROL: Female subject is post-menopausal, surgically sterilized, or willing to use acceptable methods of birth control (i.e., a hormonal contraceptive, intra-uterine device, diaphragm with spermicide, or condom with spermicide, or abstinence) for the duration of the study, and 2 weeks after completion of NEO-201 administration or 4 months after the last dose of pembrolizumab (according to package labeling), whichever is later. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately. Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 2 weeks after completion of NEO-201 administration or 4 months after the last dose of pembrolizumab (according to package labeling), whichever is later. Exclusion Criteria: * History of disseminated or uncontrolled brain metastases or central nervous system disease. Brain metastases will be considered controlled if SD on two consecutive brain MRIs, performed at least 2 months apart, and subject is without seizures. * History of allergic reactions attributed to compounds of similar chemical or biologic composition to NEO-201 or other agents used in this study. * Any major surgery within 14 days of enrollment. * Receiving any other investigational agents. * No archival tissue available and a lesion(s) that cannot be safely biopsied via percutaneous route, or is unwilling to undergo biopsy. * Has an uncontrolled concomitant illness including, but not limited to, ongoing or active infection, uncontrolled diabetes mellitus, symptomatic congestive heart failure, unstable angina pectoris, hypokalemia, family history of Long QT Syndrome or presence of cardiac arrhythmia. * Subjects who are assessed to have unacceptable risk of developing infection from neutropenia will be excluded at the Investigator's discretion. * HIV-positive subjects on combination antiretroviral therapy are ineligible because of the unknown potential for pharmacokinetic interactions with NEO-201. In addition, these subjects are at increased risk of lethal infections which could complicate the toxicity assessment of this study. Appropriate studies will be undertaken in subjects receiving combination antiretroviral therapy when indicated. * Subject has other serious medical illness, including a second malignancy, or psychiatric illness that could, in the Investigator's opinion, potentially interfere with the completion of treatment according to this protocol. * Pregnant women are excluded from this study because the potential for teratogenic or abortifacient effects due to NEO-201 is unknown. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with NEO-201, breastfeeding should be discontinued if the mother is treated with NEO-201. Additional Exclusion Criteria for Expansion Cohorts Because patients in the expansion cohort will be receiving pembrolizumab, the following additional exclusion criteria apply: * Has a diagnosis of immunodeficiency or is receiving chronic systemic steroid therapy (in dosing exceeding 10 mg daily of prednisone equivalent) or any other form of immunosuppressive therapy within 7 days prior to start of study therapy. * Active autoimmune disease that has required systemic treatment in the past 2 years (i.e. with use of disease modifying agents, corticosteroids or immunosuppressive drugs). Replacement therapy (e.g.., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency, etc.) is not considered a form of systemic treatment * Subjects who experienced severe or life-threatening immune-related AEs with prior immune checkpoint therapy requiring medical intervention (steroid or immunosuppressant drugs) and permanent discontinuation of therapy, will be excluded. These include, but not limited to colitis, autoimmune hepatitis, hypophysitis, hyperthyroidism, nephritis, myocarditis, GBS, encephalitis.