Combination Therapy for Advanced Melanoma and Kidney Cancer

* INCLUSION CRITERIA: * Participants must have histologically or cytologically confirmed cancer that falls into one of three cohorts: (1) metastatic melanoma or advanced locoregional melanoma not amenable to curative surgical resection and refractory to anti-PD-1 therapy; (2) metastatic renal cell carcinoma (clear cell histology) refractory to at least one line of PD1/PDL1 based therapy; (3) metastatic or advanced locoregional melanoma not amenable to curative surgical resection and naive to anti-PD-1 therapy. * Participants must have measurable disease (per RECIST v1.1 criteria), metastatic melanoma or renal cell cancer. * Age \>=18 years of age. * Clinical performance status of ECOG 0 or 1. * Willing to practice birth control from the time of enrollment on this study and for four months after treatment. * Must have a negative pregnancy test because of the potentially dangerous effects of the treatment on the fetus. * Seronegative for HIV antibody. (The experimental treatment being evaluated in this protocol depends on an intact immune system. Participants who are HIV seropositive may have decreased immune-competence and thus be less responsive to the experimental treatment and more susceptible to its toxicities.) * Seronegative for hepatitis B antigen and for hepatitis C antibody. If hepatitis C antibody test is positive, then participant must be tested for the presence of antigen by RT-PCR and be HCV RNA negative. * Participants must have adequate organ and marrow function as defined below: * ANC \> 1000/mm\^3 without the support of filgrastim * WBC \>= 3000/mm\^3 * Platelet count \>= 100,000/mm\^3 * Hemoglobin \> 8.0 g/d (Subject may be transfused to reach this cut-off) * Serum ALT/AST \<= 5.0 x ULN * Serum creatinine \<= 1.6 mg/dL * Total bilirubin \<= 2.0 mg/dL, except in participants with Gilbert s Syndrome, who must have a total bilirubin \< 3.0 mg/dL. * More than four weeks must have elapsed since completion of any prior systemic therapy at the time of enrollment. Note: Participant may have undergone minor surgical procedures or limited field radiotherapy within the four weeks prior to enrollment, as long as related major organ toxicities have recovered to \<= grade 1. * Ability of subject to understand and the willingness to sign a written informed consent document. * Willing to sign a Durable Power of Attorney Form. * Subject must be co-enrolled on protocol 03-C-0277 EXCLUSION CRITERIA: * Participant is nursing because of the potentially dangerous effects of the treatment on the fetus or infant. * Concurrent systemic steroid therapy. * Active systemic infections requiring anti-infective treatment, coagulation disorders, or any other active or uncompensated major medical illnesses. * Any form of primary immunodeficiency (such as Severe Combined Immunodeficiency Disease and AIDS). * History of major organ autoimmune disease. * Grade 3 or 4 major organ irAEs following treatment with anti-PD-1/PD-L1 monotherapy, including but not limited to myocarditis, pneumonitis, colitis, and hepatotoxicity. * Concurrent opportunistic infections (The experimental treatment being evaluated in this protocol depends on an intact immune system. Participants who have decreased immune-competence may be less responsive to the experimental treatment and more susceptible to its toxicities.) * History of severe immediate hypersensitivity reaction to pembrolizumab or aldesleukin. * History of coronary revascularization or ischemic symptoms. * For select participants with a clinical history prompting cardiac evaluation: last known LVEF \<= 45%. * For select participants with a clinical history prompting pulmonary evaluation: known FEV1 \<= 50%. * Participant is receiving any other investigational agents.