Cemiplimab in AlloSCT/SOT Recipients With CSCC

Inclusion Criteria: * Patients must have histologically confirmed, advanced or metastatic cutaneous squamous cell carcinoma (cSCC) with 1 or more measurable lesions (greater than or equal to 1 cm). * A history of either (Cohort 1) allogeneic hematopoietic stem cell transplant (alloHSCT) and ≥ 2 years or 730 days from day 0 of their HSCT with adequate bone marrow function (see Section 3.1.6) and off of all systemic immunosuppression (topical agents permitted) for at least 3 months prior to enrollment; sequelae of chronic graft versus host disease (GVHD) is permitted (i.e. chronic dry eyes, sclerodermatous skin changes, etc.) if the patient is not on systemic immunosuppression, or (Cohort 2) a renal transplant with a functioning allograft (at least 6 months from allograft transplant) as determined by estimated glomerular filtration (GFR) rate (CKD-EPI equation \[40\], Appendix A) ≥30 mL/min, baseline proteinuria lower than 0.5 g/day (spot urine protein-creatinine ratio), and off antiproliferative immunosuppressive medications. * Age 18 years or older. * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 (Karnofsky ≥ 60%, see Appendix B). * Participants must have adequate organ and marrow function as defined below: * leukocytes ≥ 2,200/mcL * absolute neutrophil count ≥ 1,000/mcL * platelets ≥ 90,000/mcL * total bilirubin within normal institutional limits (except in cases where Gilbert syndrome is known or suspected, where total bilirubin should be \< 3 mg/dL) * AST(SGOT)/ALT(SGPT) ≤ 2.5 × institutional upper limit of normal * creatinine ≤ 1.5 × institutional upper limit of normal OR * estimated GFR ≥ 30 mL/min/1.73 m2 for participants with creatinine levels above institutional normal (CKD-EPI equation). * urine protein/creatinine ratio \< 0.5 (equal to less than 500 mg of proteinuria per day) * Ability to understand and the willingness to sign a written informed consent document. * A prior history of acute GVHD that has resolved, or sequelae of chronic GVHD following allo-HSCT is permitted. Active acute GVHD patients are excluded. * Women of childbearing potential (WOCBP) must agree to use at least 1 highly effective form of contraception (refer to Appendix C for examples). WOCBP should plan to use an adequate method to avoid pregnancy for up to 7 months (30 days plus the time required for cemiplimab to undergo five half-lives) after the last dose of investigational drug. "Women of childbearing potential (WOCBP)" is defined as any female who has experienced menarche, who has not undergone surgical sterilization (hysterectomy or bilateral oophorectomy), who is not postmenopausal, who is sexually active with a male partner. Menopause is defined clinically as 12 months of amenorrhea in a woman over 45 in the absence of other biological or physiological causes. In addition, women under the age of 55 must have a documented serum follicle stimulating hormone (FSH) level less than 40 mIU/mL. * Women of childbearing potential, as defined above, must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of HCG) within 24 hours prior to the start of cemiplimab. * Men who are sexually active with WOCBP must agree to use any contraceptive method with a failure rate of less than 1% per year. Men who are sexually active with WOCBP will be instructed to adhere to contraception for a period of 7 months after the last dose of investigational product. Women who are not of childbearing potential as defined above, and azoospermic men) do not require contraception. See Appendix C for further guidance on contraception Exclusion Criteria: * Participants who have had chemotherapy or radiotherapy within 3 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have unresolved toxicities from prior anti-cancer therapy more than 4 weeks earlier, defined as not resolved to National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events (CTCAE, version 5.0), grade 0 or 1. * Participants who are receiving any other investigational agents. * For Cohort 1 allo-HSCT patients enrolling to the study, corticosteroid doses \> 10 mg of prednisone daily or equivalent within 4 weeks of the first dose of PD-1 inhibitor are prohibited. For Cohort 2 renal transplant patients enrolling to the study, corticosteroid use is permitted if used as part of their immunosuppressive regimen for graft protection prior to enrollment. * Existing significant autoimmune conditions. Patients with a history of Hashimoto thyroiditis who are stable on replacement hormone therapy are not excluded. * Known human immunodeficiency virus carrier or a diagnosis of immunodeficiency. Any positive test result for hepatitis B virus or hepatitis C virus indicating presence of virus, e.g., Hepatitis B surface antigen (HBsAg, Australia antigen) positive, or Hepatitis C antibody (anti-HCV) positive (except if HCV-RNA negative). * Kidney transplant recipients with active acute rejection. * Allergy to cemiplimab or any of its components. * Any prior exposure to the phosphoinositide 3-kinase inhibitor idelalisib. * Subject who has been treated with immunotherapy. This includes prior treatment with anti-PD-1, anti-PD-L1, anti-PD-L2, anti-CTLA-4 antibody, or any other antibody or drug specifically targeting T-cell co-stimulation or checkpoint pathways (including chimeric antigen receptor \[CAR\] T cell therapies). Prior topical or intralesional immunotherapies (e.g. imiquimod, talimogene laherparepvec) are allowed. * Subject with known and untreated brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. However, baseline brain imaging is not required prior to enrollment in the study if patients are asymptomatic. Patients at least 4 weeks out from metastatic central nervous system (CNS) treatment are permitted to enroll, if they are asymptomatic, radiographically stable per the investigator, and on stable doses of anti-epileptic drugs (AEDs) and oral corticosteroids (for Cohort 1 only, the patient must be on 10 mg of prednisone daily equivalent dosing or less, see 3.2.2) at the time of enrollment. * Participants receiving any medications or substances that are strong inhibitors or inducers of CYP3A4 are ineligible. Because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated list such as \[http://medicine.iupui.edu/clinpharm/ddis/table.aspx\]. Medical reference texts such as the Physicians' Desk Reference may also provide this information. As part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, or cardiac arrhythmia. * Known non-infectious pneumonitis or any history of interstitial lung disease.