This phase I/II trial studies the side effects and best dose of entinostat when given together with aldesleukin and to see how well this works in treating patients with kidney cancer that has spread to other places in the body. Entinostat may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Aldesleukin may stimulate the white blood cells to kill kidney cancer cells. Giving entinostat together with aldesleukin may be a better treatment for metastatic kidney cancer.

PRIMARY OBJECTIVES:

I. To evaluate the safety and tolerability of high dose interleukin 2 (aldesleukin) in combination with entinostat in patients with metastatic renal cell carcinoma (RCC). (Phase I) II. To monitor toxicity and estimate the efficacy of high dose aldesleukin combined with entinostat in patients with metastatic RCC. (Phase II)

SECONDARY OBJECTIVES:

I. To compare the time-to-tumor progression, progression-free survival and overall survival of patients with metastatic RCC treated with high dose aldesleukin combined with entinostat to the historical data of patients treated with high dose aldesleukin alone. (Phase II) II. To assess the toxicity of high dose aldesleukin combined with entinostat. (Phase II) III. To evaluate entinostat pharmacodynamics (PD) in blood and tumor samples. (Phase II) IV. To measure the association between baseline laboratory parameters (e.g. cluster of differentiation [CD]4+, CD8+, CD4+/forkhead box P3 [Foxp3]), tumor blood metabolism, and a variety of response variables (e.g. toxicity, response and survival). (Phase II) V. To explore the relationship between entinostat exposure with PD endpoints (e.g. toxicity and histone acetylation in peripheral blood mononuclear cells or peripheral blood mononuclear cells [PBMNCs] and changes in T cell subset population). (Phase II) VI. To evaluate the modulation of tumor metabolism by fluorodeoxyglucose (FDG, fludeoxyglucose F 18) positron emission tomography (PET)/computed tomography (CT) scan. (Phase II)

OUTLINE: This is a phase I, dose-escalation study of entinostat followed by a phase II study.

Patients receive entinostat orally (PO) every 2 weeks beginning on day -14 and high-dose aldesleukin intravenously (IV) every 8 hours on days 1-5 and 15-19. Cycles repeat every 84 days* in the absence of disease progression or unacceptable toxicity.

NOTE: *Patients with evidence of tumor shrinkage may receive up to 3 cycles of high-dose aldesleukin therapy. Patients with stable disease by Response Evaluation Criteria in Solid Tumors (RECIST) version 1.0 criteria, but without evidence of tumor shrinkage after two cycles will receive only entinostat until disease progression is documented.

After completion of study treatment, patients are followed up at 30 days and then every 3 months thereafter.

Inclusion Criteria:

• Patients must have pathological diagnosis of renal cell carcinoma that is metastatic or surgically unresectable; the histology must be clear cell carcinoma or predominant clear cell carcinoma
• Patients may have received up to two prior therapies including vascular endothelial growth factor (VEGF), mammalian target of rapamycin (mTOR) and programmed cell death (PD)-1/PD ligand 1 (L1) inhibitors; prior palliative radiation to metastatic lesion(s) is permitted, provided there is at least one measurable and/or evaluable lesion(s) that has not been irradiated
• Patients must have measurable or evaluable disease
• Eastern Cooperative Oncology Group (ECOG) performance status 0
• Life expectancy of greater than 6 months
• Hemoglobin >= 12 g/dL
• Leukocytes >= 3,000/mm^3
• Absolute neutrophil count >= 1,500/mm^3
• Platelets >= 100,000/mm^3
• Total bilirubin =< 1.5 x laboratory upper limit of normal
• Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase [SGOT])/alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase [SGPT]) =< 2.5 x laboratory upper limit of normal
• Creatinine =< 1.5 x laboratory upper limit of normal or calculated creatinine clearance of >= 50 ml/min
• Lactate dehydrogenase (LDH) within normal limits (WNL)
• Corrected calcium =< 10 mg/dL
• Prothrombin time (PT)/international normalized ratio (INR) =< 1.5
• Urine protein < 1+; if >= 1+, 24 hour urine protein should be obtained and should be < 1000 mg
• Forced expiratory volume in 1 second (FEV1) >= 2.0 liters or >= 75% of predicted for height and age; (pulmonary function tests [PFTs] are required for patients over 50 or with significant pulmonary or smoking history)
• No evidence of congestive heart failure, symptoms of coronary artery disease, myocardial infarction less than 6 months prior to entry, serious cardiac arrhythmias, or unstable angina; patients who are over 40 or have had previous myocardial infarction greater than 6 months prior to entry will be required to have a negative or low probability cardiac stress test for cardiac ischemia
• No history of cerebrovascular accident or transient ischemic attacks
• The effects of entinostat on the developing human fetus at the recommended therapeutic dose are unknown; for this reason Women of child-bearing potential must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately; men with female partners of child bearing potential must also agree to use adequate contraception
• Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

• Patients who have received more than two prior therapies
• Concurrent use of valproic acid is not allowed
• Patients may not be receiving any other investigational agents
• Patients with untreated central nervous system (CNS) metastases; patients should have a head CT/magnetic resonance imaging (MRI) within 28 days prior to treatment initiation; patients with previously excised/gamma knifed solitary or oligometastases and controlled disease are eligible
• Any medical condition that would preclude adequate evaluation of the safety and toxicity of the study combination
• Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure (New York Association class II, III, or IV), angina pectoris requiring nitrate therapy, recent myocardial infarction (< the last 6 months), cardiac arrhythmia, history of cerebrovascular accident (CVA) within 6 months, hypertension (defined as blood pressure of > 160 mmHg systolic and/or > 90 mmHg diastolic on medication) history of peripheral vascular disease, or psychiatric illness/social situations that would limit compliance with study requirements
• Patients with a history of allergy to entinostat or other medications that have a benzamide structure (i.e. tiapride, remoxipride, and clebopride)
• Pregnant women are excluded from this study; breastfeeding should be discontinued if the mother is treated with entinostat
• Human immunodeficiency virus (HIV)-positive patients receiving combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with entinostat. In addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy; appropriate studies will be undertaken in patients receiving combination anti-retroviral therapy when indicated
• Serious or non-healing wound, ulcer or bone fracture
• Major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to day 1 therapy
• Anticipation of need for major surgical procedures during the course of the study
• Left ventricular ejection function < 45%