RPTR-168 in Patients With Human Papillomavirus Strain 16 (HPV-16) E6/E7 Positive Tumors and Melanoma

INCLUSION CRITERIA: Patients eligible for inclusion in this study must meet all of the following criteria: 1. Be willing and able to provide written informed consent for the trial. 2. Written informed consent must be obtained prior to any study procedures. 3. Age ≥18 years. 4. Patients must have one of the following histologically- or cytologically-confirmed, relapsed/refractory, and metastatic or locally advanced solid tumor types and their disease must have has progressed despite all appropriate curative or life-prolonging treatments, unless they are intolerant to these therapies or have refused standard treatment. 1. Malignant melanoma for RPTR-168:1 therapy. Patients with non-cutaneous melanoma must have PRAME positive tumor, as determined by a qualified laboratory. For patients with PRAME negative tumors, the Investigator must consult with the Sponsor medical monitor about the suitability of an individual patient for enrollment. 2. HPV-16 E6/E7 positive tumors for RPTR-168:2 therapy. 5. Failure to respond to standard therapy, or for whom no appropriate therapies are available (based on the judgment of the Investigator). 1. For melanoma patients, the definition of failure to respond an approved therapy for recurrent or metastatic disease is the following: * Tumor refractory to or progressing following prior PD-1/PD-L1 therapy alone or in combination with an anti-CTLA-4 agent unless the patient was deemed ineligible for such treatment. * If a subject is BRAF V600E/K positive, they must have received an approved BRAF- targeted regimen prior to entering the study, unless the patient was deemed ineligible for such treatment. * Prior adjuvant therapy cannot be used to define prior treatment failure. 2. For head and neck cancer patients, the definition of failure to respond to standard therapy is tumor refractory to or progressing following approved first- and second-line therapy for metastatic or recurrent disease consisting of one or more of the following: * PD-1/PD-L1 therapy alone or in combination unless the patient was deemed ineligible for such treatment. * Cetuximab therapy alone or in combination unless the patient was deemed ineligible for such treatment. * Prior adjuvant or neo-adjuvant therapy cannot be used to define prior treatment failure. 3. For cervical cancer patients, the definition of failure to respond to an approved therapy for recurrent or metastatic disease is the following: * For all patients: Tumor refractory to or progressing following prior treatment with a platinum-based chemotherapy. * For PD1 expressing tumors: Tumor refractory to or progressing following prior PD-1/PD-L1 therapy alone or in combination. 4. For anal and penile cancer patients the definition of failure to respond to an approved therapy for recurrent or metastatic disease is the following: \- Tumor refractory to or progressing following prior treatment with a platinum-based chemotherapy. 5. For vulvar cancer patients a patient must no longer be a candidate for local/regional therapy 6. Able to provide a buccal swab to undergo HLA typing, or submit documented HLA typing from a previously performed test, to be reviewed and approved by the Sponsor. 7. For patients undergoing screening to receive RPTR-168:2 therapy, patients must have archival tumor tissue or be able to undergo a fresh tumor biopsy to submit tissue for HPV testing, as well as profiling of DNA, RNA and proteins. HPV-16 E6/E7 positivity in the patient's tumor tissue must be established using a validated clinical trial assay performed in a CLIA/CAP accredited reference laboratory. If documented results of HPV-16 E6/E7 are available from a previous test, the patient can be enrolled using these results after review and approval by the Sponsor. 8. Patients must have measurable disease per mRECIST 1.1 as determined by radiologic evaluations or tumor assessments obtained within 2 months prior to study entry. 1. If there are no pre-existing radiologic assessments within 2 months prior to study entry available, other evidence of measurable disease may be considered sufficient to fulfill this criterion following documented discussion and approval from the Sponsor. 2. Please note, patients must have a radiological/tumor assessment per mRECIST v1.1 within 28 days prior to receiving study therapy to serve as the patient's baseline tumor assessment. 9. Eastern Cooperative Oncology Group (ECOG) Performance Status ≤1. 10. Patient must be willing and able to provide a tumor tissue sample prior to the start of study therapy and once during study therapy. 1. For the pre-dose tumor sample, a fresh tumor biopsy obtained prior to the start of study therapy is preferred, but an archival sample (collected within ≤ 2 months prior to the start of study therapy) may be submitted. 2. For the on-treatment tumor sample, the patient must be willing and able to have a fresh tumor biopsy to collect tissue for submission. 11. A female participant is eligible to participate if she is not pregnant, not breastfeeding, and at least one of the following conditions applies: 1. Not a woman of childbearing potential (WOCBP), defined as all women physiologically capable of becoming pregnant. 2. A WOCBP who agrees to follow contraceptive guidance during the treatment period and for at least 120 days after the last dose of study treatment. A serum pregnancy test must be performed during screening to confirm the patient is not pregnant. 12. A male participant must agree to use contraception during the treatment period and for at least 120 days after the last dose of study treatment. EXCLUSION CRITERIA: Patients eligible for this study must not meet any of the following criteria: 1. Previously identified hypersensitivity to components of the study treatment or excipients. 2. Presence of active CNS disease and/or carcinomatous meningitis. Participants with previously treated brain metastases may participate provided they are radiologically stable, i.e., without evidence of progression for at least 4 weeks by repeat imaging (note that the repeat imaging should be performed during study screening), clinically stable, and without requirement of steroid treatment for at least 14 days prior to study entry. 3. Has received prior radiotherapy within 2 weeks prior to study entry. Participants must have recovered from all radiation-related toxicities, not require corticosteroids, and not have had radiation pneumonitis. A 1-week washout is permitted for palliative radiation (≤2 weeks of radiotherapy) to non-CNS disease. The target lesions must not be irradiated. 4. Patient having out of range laboratory values defined as: 1. Creatinine clearance (calculated using Cockcroft-Gault formula, or measured) \<40 mL/min 2. Total bilirubin \>1.5 x upper limit of normal (ULN), except for patients with Gilbert's syndrome who are excluded if total bilirubin \>3.0 x ULN or direct bilirubin \>1.5 x ULN 3. Alanine aminotransferase (ALT) and Aspartate aminotransferase (AST) \>2 x ULN, except for patients that have tumor involvement of the liver, who are excluded if ALT and AST \>3 x ULN. ALT and AST up to 5x ULN may be considered with documented discussion and approval from sponsor. 4. Absolute neutrophil count (ANC) ≤1.0 x 109/L 5. Absolute lymphocyte count ≤0.5 x 109/L. Patients with ALC counts ≤0.5 x 109/L may be considered for inclusion after discussion and approval by the sponsor medical monitor. 6. Platelet count ≤75 x 109/L absent platelet transfusion for 2 weeks 7. Hemoglobin (Hgb) ≤9 g/dL absent RBC transfusion for 2 weeks 8. Coagulation (prothrombin time \[PT\] or international normalized ratio \[INR\] and partial thromboplastin time \[PTT\] or activated partial thromboplastin time \[aPTT\]) \- \>1.5 × ULN unless participant is receiving anticoagulant therapy as long as PT/INR and PTT/aPTT is within therapeutic range of intended use of anticoagulants 9. Potassium, magnesium, calcium or phosphate abnormality \> Grade 1 (CTCAE v5.0) despite appropriate oral replacement therapy: 10. Serum triglycerides \>500 mg/dL due to potential interference with cell separation methods 5. Clinically significant and/or uncontrolled heart disease such as congestive heart failure requiring treatment (New York Heart Association \[NYHA\] Grade ≥2), uncontrolled hypertension, or clinically significant arrhythmia. 6. Acute myocardial infarction or unstable angina pectoris \<6 months prior to study entry. 7. Patients with active, known or suspected autoimmune disease that has required systemic treatment in the past 2 years (i.e., with use of disease modifying agents, corticosteroids, or immunosuppressive drugs). 1. Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment and is allowed. 2. Patients with vitiligo, type 1 diabetes mellitus, residual hypothyroidism due to autoimmune condition only requiring hormone replacement, psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are permitted to enroll. 8. Has a history of (non-infectious) pneumonitis that required steroids or has current pneumonitis. 9. 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 study entry. 10. Has a known additional malignancy that is progressing or has required active treatment within the past 3 years. Note: Participants with basal cell carcinoma of the skin, squamous cell carcinoma of the skin, or carcinoma in situ (e.g., breast carcinoma, cervical cancer in situ) that have undergone potentially curative therapy are not excluded. 11. Has a known history of human immunodeficiency virus (HIV) infection. No HIV testing is required unless mandated by local health authority. 12. Documented history of Hepatitis B (defined as Hepatitis B surface antigen \[HBsAg\] reactive) or known active Hepatitis C virus (defined as HCV RNA \[qualitative\] is detected) infection. Note: No testing for Hepatitis B and Hepatitis C is required unless mandated by local health authority. 13. Malignant disease, other than that being treated in this study expected to interfere with the assessment of efficacy in the opinion of the investigator. 14. Active infection requiring systemic therapy. 15. Patients requiring chronic treatment with systemic steroid therapy, other than replacement dose steroids in the setting of adrenal insufficiency. Topical, inhaled, nasal, or ophthalmic steroids are allowed. 16. Patients receiving systemic treatment with any other immunosuppressive medication. 17. Use of any live vaccines against infectious diseases within 30 days of study entry. Examples of live vaccines include, but are not limited to, the following: measles, mumps, rubella, varicella/zoster (chicken pox), yellow fever, rabies, Bacillus Calmette-Guérin (BCG), and typhoid vaccine. Seasonal influenza vaccines for injection are generally killed virus vaccines and are allowed; however, intranasal influenza vaccines (e.g., FluMist®) are live attenuated vaccines and are not allowed. 18. Major surgery within 4 weeks of study entry (mediastinoscopy, insertion of a central venous access device, and insertion of a feeding tube are not considered major surgery). Note: If participant received major surgery, they must have recovered adequately from the toxicity and/or complications from the intervention. 19. Is currently participating in or has participated in a study of an investigational agent or has used an investigational agent or device within 4 weeks prior to the first dose of study drug. Note: Patients participating in another investigational study, or receiving standard of care treatment, may consent to having archival tumor tissue sent for testing (eg, to assess HPV-16 E6/E7 status). 20. Presence of ≥ Grade 2 (CTCAE v5.0) toxicity from prior therapy (except alopecia, peripheral neuropathy, and ototoxicity, which are excluded if ≥ Grade 3 \[CTCAE v5.0\]) due to prior cancer treatment. a. Patients who were required to discontinue PD-1/PD-L1, CTLA-4, or other immunomodulatory antibodies due to ≥Grade 3 irAE may be included following discussion with the Sponsor. 21. Patients who received prior T-cell anti-cancer vaccines and T-cell therapies are excluded. 22. Has undergone prior allogeneic HSCT 23. Patients with rapidly progressing disease that would preclude waiting 4-6 weeks after apheresis to receive study therapy. 24. Prior therapy with PD-1/PDL-1, CTLA-4 or other immunomodulatory antibodies inhibitors ≤2 weeks prior to the apheresis procedure. 25. Systemic anti-cancer therapy within 5 half-lives or 2 weeks; whichever occurs first, prior to the apheresis procedure. 1. Systemic cytotoxic agents that have major delayed toxicity, e.g. mitomycin C and nitrosoureas, ≤6 weeks prior to study entry. 2. Participants must have recovered from all AEs due to previous therapies to ≤Grade 1 or baseline. Participants with ≤Grade 2 neuropathy may be eligible. 26. Has a history or current evidence of any condition, therapy, or laboratory abnormality that might confound the results of the study, interfere with the participant's participation for the full duration of the study, or is not in the best interest of the participant to participate, in the opinion of the treating investigator. 27. Has known psychiatric or substance abuse disorders that would interfere with cooperating with the requirements of the study. 28. Is pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the study, starting with the screening visit through 120 days after the last dose of study treatment.