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 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.

               2. HPV-16 E6/E7 positive tumors (Head & Neck Squamous Cell Carcinoma [HNSCC],
                  cervical cancer) 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 (programmed cell
                       death protein 1)/PD-L1 (programmed death-ligand 1) therapy alone or in
                       combination with an anti-CTLA-4 (cytotoxic T-lymphocyte-associated protein
                       4) agent unless the patient was deemed ineligible for such treatment.

                    -  If a subject is BRAF (v-Raf murine sarcoma viral oncogene homolog B) 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 PD-1 expressing tumors: Tumor refractory to or progressing following
                       prior PD-1/PD-L1 therapy alone or in combination.

          6. Able to provide a buccal swab to undergo human leukocyte antigen (HLA) typing at a
             central lab. The specific HLA types for inclusion in the study will be determined by
             the Sponsor based on emerging data and will be updated on an ongoing basis. If
             documented HLA results are available from a previous test, the patient can be enrolled
             using these results after review and approval 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 Clinical Laboratory Improvement Amendments (CLIA)/College of American
             Pathologists (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. Patient must have measurable disease per modified Response Evaluation Criteria in
             Solid Tumors (mRECIST) v 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/tumor 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 with 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.

             Please refer to the full protocol (Section 7.2.4) for information on the collection
             schedule and parameters. Additional details regarding tumor sample acquisition and
             processing can be found in the study laboratory manual(s).

         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 are ineligible for this study if they meet any of the following criteria:

          1. Previously identified hypersensitivity to components of the study treatment or
             excipients.

          2. Presence of active central nervous system (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 (ALC) ≤1.0 x 109/L

               6. Platelet count ≤75 x 109/L absent platelet transfusion for 2 weeks

               7. Hemoglobin (Hgb) ≤9 g/dL absent red blood cell (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 (common
                  terminology criteria for adverse events [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 device within 4 weeks prior to study entry.

             Note: Participants who have entered the follow-up phase of an investigational study
             may participate as long as it has been 4 weeks after the last dose of the previous
             investigational agent.

         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 immune-related adverse event (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 hematopoietic stem cell transplantation (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/PD-L1, 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.