Immunotherapy in Combination With Prednisone and Sirolimus for Kidney Transplant Recipients With Unresectable or Metastatic Skin Cancer

Inclusion Criteria: * Patients must be kidney transplant recipients with a functioning allograft who do not currently require dialysis * Patient's age must be \>= 18 years. Because no dosing or adverse event (AE) data are currently available on the use of nivolumab and ipilimumab in kidney transplant recipients \<18 years of age, children are excluded from this study, but may be eligible for future pediatric trials * Patients must have histologically or cytologically confirmed non-uveal melanoma, basal cell carcinoma, Merkel cell carcinoma, or cutaneous squamous cell carcinoma for which standard non-immunological medical, surgical, or radiation therapy would be insufficient (i.e., patients who are not surgical candidates). Patients with cutaneous squamous cell carcinoma or Merkel cell carcinoma may enroll without prior medical therapy (e.g., cetuximab or chemotherapy respectively). Non-immunologic standard therapies that patients must have received, refused or for which patients were ineligible include: * For patients with BRAF-mutant melanoma, prior therapies include BRAF/MEK inhibitors * For patients with Basal cell carcinoma, prior therapies include hedgehog pathway inhibitors * Patients must have measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 criteria, i.e., at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) …