Combining two immunotherapies for advanced melanoma and renal cell carcinoma

* 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.