Study to Investigate the Efficacy and Safety of RP1 in Adult Patients With Organ Transplants and Advanced Skin Malignancies

Key Inclusion Criteria: 1. Voluntary agreement to provide written informed consent prior to any study procedures and the willingness and ability to comply with all aspects of the protocol and understand the risk to their organ allograft. 2. Male or female at birth and at least 18 years of age prior to signing informed consent. 3. Solid organ or allogeneic hematopoietic cell transplant patients with histologically or cytologically confirmed recurrent, cutaneous malignancies including locally advanced CSCC, metastatic (to skin, soft tissue, or lymph nodes) or locally advanced BCC, metastatic or locally advanced MCC, and melanoma. 4. Patients must have progressed or experienced recurrence from previous local resection and/or prior radiation. 5. Documentation from the patient's transplant physician confirming that the patient's allograft is stable. For dual transplant recipients, a failure of 1 of the transplanted organs is allowed. 6. Patients for whom surgical or radiation treatment of lesions is contraindicated or are considered to be inoperable. 7. Patients must have at least 1 measurable tumor of at least 1 cm in longest diameter. All measurable lesions identified at screening must be injectable and planned to be injected during the course of the study. 8. ECOG performance status of at most 1. 9. Adequate allograft function as determined by functional testing and as confirmed by the transplant clinician. 1. For renal transplant recipients, patients must have serum creatinine increase of \< 30% mean increase over the past 6 months. 2. For lung transplant recipients, patients must have stable forced exploratory volume in 1 second (FEV1) of at least 50% predicted with no more than a 10% decline in the absolute FEV1 over the past 12 months. 3. For cardiac transplant recipients, patients must have: ci. At least 50% ejection fraction with not more than an absolute change of 5% over the past 12 months. If the absolute change in ejection fraction is greater than 5% and there is no clinical suspicion for rejection by the transplant center, left ventricular ejection fraction (LVEF) stability needs to be shown by a repeat echo within 28 days after the most recent ECHO. cii. No evidence of hemodynamically or angiographically significant cardiac allograft vasculopathy (CAV) (i.e., patients must not have CAV2 or CAV3), or no ischemia by appropriate diagnostic imaging over the past 12 months. 4. For patients with stable pancreas transplant, amylase and lipase should be ≤ 3 x upper limit of normal (ULN) for at least 6 months prior to enrollment. 10. Adequate hepatic function 11. Adequate renal function as indicated by a serum creatinine or estimated glomerular filtration rate (eGFR) determined based on the Chronic Kidney Disease-Epidemiology Collaboration equation. 12. Adequate hematologic function 13. Adequate coagulation parameters 14. Anticipated life expectancy \> 6 months. 15. Have provided either formalin-fixed, paraffin-embedded (FFPE) tissue block and/or unstained tumor tissue sections, obtained within 90 days prior to enrollment, with an associated pathology report, which must be submitted to the central laboratory for inclusion or a fresh excisional, incisional, or core needle biopsy taken prior to dosing on C1D1 if an archival biopsy (collected within 90 days prior to enrollment) is not available. 16. Female and male patients (at birth) who meet the following criteria: 1. Female patients are eligible if not pregnant or breastfeeding and if one of the following applies 1) is a woman of non-childbearing potential (WNCBP) OR 2) is a woman of childbearing potential (WOCBP) and must agree to use a highly effective contraception method during the treatment period and for at least 90 days after last dose of RP1. 2. Male patients are eligible if they agree to the following during the study intervention period and for at least 90 days after the last dose of RP1: refrain from donating fresh unwashed semen plus either be abstinent from intercourse where pregnancy can occur OR must agree to use external condom and advise their partner to use a highly effective method of contraception. Key Exclusion Criteria: 1. Prior treatment with an oncolytic therapy or checkpoint inhibitor. 2. Patients with visceral metastases. 3. Active significant herpetic infections or prior complications of HSV-1 infection (e.g., herpetic keratitis or encephalitis). Patients requiring use of systemic (oral/intravenous \[IV\]) antiviral agents with known antiherpetic activity. 4. Patients requiring concurrent treatment with cytotoxic T-lymphocyte antigen 4-Ig (CTLA-4-Ig) medications. 5. Had systemic infection requiring IV antibiotics or other serious infection within 14 days prior to dosing. 6. Patients with an active, known, or suspected autoimmune disease that requires systemic immunosuppressive treatment beyond immunosuppressive medications required for maintenance of allograft rejection prevention. 7. Patients with a history of any positive test result for hepatitis B virus (HBV) or hepatitis C virus (HCV) indicating the presence of the virus, or human immunodeficiency virus (HIV) positive. Patients with a history of HBV or HCV must have undetectable viral load within 3 months of study entry. 8. A history of transplant-related viral infections such as BK virus (BKV), Epstein-Barr virus (EBV), or cytomegalovirus (CMV) requiring treatment or modification to immunosuppression within 3 months of study entry. 9. Had clinically significant cardiovascular disease within 6 months from first dose of RP1, including New York Heart Association Class III or IV congestive heart failure, unstable angina, myocardial infarction or stroke/transient ischemic attack or significant cardiac arrhythmias associated with hemodynamic instability. 10. Radiation therapy within 14 days of first dose of RP1, or topical or any systemic therapy within 30 days of the first dose of RP1. 11. Documented history of allergic reactions or acute hypersensitivity reaction attributed to RP1 or to any of the excipients. 12. Females who have a positive serum beta-human chorionic gonadotropin (β-hCG) test for pregnancy (at screening within 72 hours before dosing), or a positive urine pregnancy test on C1D1. 13. Any active malignancy within 3 years of the date of first planned dose of RP1, except for the specific cancer under investigation in this study and tumors with negligible risk of metastasis or death. 14. Any acute or chronic psychiatric problems, alcohol abuse, or substance abuse disorders that, in the opinion of the investigator, would interfere with the patient's ability to comply with the requirements of the study. 15. Any co-morbidity, physical examination finding, metabolic dysfunction, or clinical laboratory abnormality that, in the opinion of the investigator, renders the patient unsuitable for participation due to safety risks or potential to affect interpretation of results of the study. 16. Treatment with botanical preparations (e.g., herbal supplements or traditional Chinese medicines) intended for general health support or to treat the disease under study within 2 weeks prior to the first dose and throughout the study. 17. Has received a live vaccine within 30 days prior to the first dose of study drug. Note: Available COVID-19 vaccines do not contain live virus. 18. Active or history of leptomeningeal disease or brain metastasis. 19. Active graft versus host disease greater than Grade 1 within the last 12 months requiring systemic treatment.