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

PRIMARY OBJECTIVE: I. To evaluate the proportion of kidney transplant recipients with selected advanced cutaneous cancers who at 14 weeks after administration of prednisone, sirolimus, nivolumab, and ipilimumab experience complete response (CR), partial response (PR), or stable disease (SD) without allograft loss. SECONDARY OBJECTIVE: I. To estimate the objective response rate (ORR), rate of allograft loss, and durations of progression-free survival (PFS) and overall survival (OS) in the study population. EXPLORATORY OBJECTIVES: I. To characterize correlates of the host immune response including, but not limited to: Ia. Histopathological characteristics of allograft rejection/loss; Ib. Immunological changes in the tumor microenvironment (e.g., changes in T-cell subset populations or expression of immune checkpoint molecules) in paired biopsies obtained pre-treatment and on-treatment; Ic. Characteristics of anti-programmed death-1 (PD-1)-associated immune-mediated adverse reactions (IMARs) in this patient population treated with immunosuppression; Id. To identify upregulated immune-related genes using multiplex quantitative reverse transcription polymerase chain reaction (qRT-PCR). II. To observe whether changes in donor-derived cell-free deoxyribonucleic acid (DNA) (dd-cfDNA) as a marker for allograft rejection. III. To compare baseline patient allograft/donor characteristics, to include human leukocyte antigen (HLA) status, date of transplant, presence of donor specific antibodies, history of prior rejection, and Calculated Panel Reactive Antibodies score, in patients who experience and do not experience rejection while on this study. IV. To observe the objective response rate (ORR) of patients who achieve PR/CR or stable disease for \>= 6 months with eventual progressive disease requiring re-induction with nivolumab + ipilimumab (receive \> 4 doses of nivolumab + ipilimumab). OUTLINE: Patients receive sirolimus orally (PO) and prednisone PO daily, starting 7 days prior to cycle 1 day 1 of immunotherapy. Patients also receive nivolumab intravenously (IV) over 30 minutes and ipilimumab IV over 30 minutes on day 8 of cycle 1 and day 1 of cycle 2. Six weeks after the first dose of nivolumab and ipilimumab, patients undergo tumor response assessment. Patients who achieve stable disease (SD), partial response (PR), or complete response (CR) receive nivolumab IV on day 1 of each cycle. Cycles repeat every 4 weeks for a total of 24 cycles in the absence of disease progression or unacceptable toxicity. Patients who had disease progression at this time or any time on trial may receive nivolumab IV and ipilimumab IV on day 1 of each cycle. Cycles repeat every 3 weeks for 2 cycles, in the absence of unacceptable toxicity. Patients are then assessed for tumor response again after 6 weeks and receive nivolumab monotherapy if they achieve SD, PR, or CR. If patients have progressive disease, they may receive nivolumab monotherapy or discontinue study treatment. Patients may undergo magnetic resonance imaging (MRI) during screening, undergo tumor biopsy on study and undergo computed tomography (CT) scan and blood sample collection throughout the study. Patients may undergo kidney biopsy if rejection is suspected. Patients follow up every 12 weeks for 1 year after stopping therapy, then every 16 weeks for the second year after stopping and then every 20 weeks for up to 5 years.