Sitravatinib and Nivolumab in Treating Patients With Advanced or Metastatic Kidney Cancer

Inclusion Criteria: * Patients with histologically or cytologically confirmed metastatic/advanced clear cell RCC, or RCC with a clear cell component, who have received 1 or 2 prior anti-angiogenic therapy regimens (+/- cytokine therapy with interleukin-2 or interferon-alfa) in the advanced or metastatic setting; examples of anti-angiogenic agents include, but are not limited to, sorafenib, sunitinib, pazopanib, axitinib, and bevacizumab * There must be evidence of progression on or after last treatment regimen received and within 6 months of enrollment * Patients must have at least one measurable site of disease, defined as a lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) and measures \>= 15 mm with conventional techniques or \>= 10 mm with more sensitive techniques such as magnetic resonance imaging (MRI) or spiral computed tomography (CT) scan; if the patient has had previous radiation to the marker lesion(s), there must be evidence of progression since the radiation * Karnofsky performance status \>= 70 * Hemoglobin \>= 9 g/dl (treatment allowed) (within 14 days prior to study entry) * Absolute neutrophil count \>= 1,500/uL (within 14 days prior to study entry) * Platelets \>= 100,000/uL (within 14 days prior to study entry) * Total bilirubin =\< 1.5 mg/dl (within 14 days prior to study entry) * Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) or alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 x institutional upper limit of normal (ULN), except in known hepatic metastasis, wherein may be \< 5 x ULN (within 14 days prior to study entry) * Serum creatinine =\< 1.5 x ULN (as long as patient does not require dialysis); a) may receive transfusion b) if creatinine is not \< 1.5 x ULN, then calculate by Cockcroft-Gault methods or local institutional standard and creatinine clearance (CrCl) must be \>= 40 mL/kg/1.73 m\^2 (within 14 days prior to study entry) * International normalized ratio (INR) and partial thromboplastin time (PTT) =\< 1.5 x ULN within 14 days prior to study entry; therapeutic anticoagulation with warfarin is allowed if target INR =\< 3 on a stable dose of warfarin or on a stable dose of low molecular weight (LMW) heparin for \> 2 weeks (14 days) at the time of enrollment * Female patients of childbearing potential (not postmenopausal for at least 12 months and not surgically sterile) must have a negative serum or urine pregnancy test (minimum sensitivity 25 IU/L or equivalent units of human chorionic gonadotropin \[HCG\]) within 14 days before study entry; pregnancy test must be repeated if performed \> 14 days before starting study drug * Women must not be breastfeeding * Patients with a history of major psychiatric illness must be judged (by the treating physician) able to fully understand the investigational nature of the study and the risks associated with the therapy * Patients with controlled brain metastases are allowed on protocol if they had solitary brain metastases that was surgically resected or treated with radiosurgery or gamma knife, without recurrence or edema for 1 month (4 weeks) Exclusion Criteria: * Patients must not have any other malignancies within the past 2 years except for in situ carcinoma of any site, or adequately treated (without recurrence post-resection or post-radiotherapy) carcinoma of the cervix or basal or squamous cell carcinomas of the skin or active non-threatening second malignancy that would not, in the investigator's opinion, potentially interfere with the patient's ability to participate and/or complete this trial; examples include but not limited to: urothelial cancer grade Ta or T1, adenocarcinoma of the prostate treated by active surveillance * Patients currently receiving anticancer therapies or who have received anticancer therapies within 2 weeks (14 days) from enrollment into this study (including chemotherapy and targeted therapy) are excluded; also, patients who have completed palliative radiation therapy more than 14 days prior to the first dose of MGCD516 are eligible * Patients, who have had a major surgery or significant traumatic injury (injury requiring \> 4 weeks \[28 days\] to heal) within 4 weeks (28 days) of start of study drug, patients who have not recovered from the side effects of any major surgery (defined as requiring general anesthesia) or patients that are expected to require major surgery during the course of the study * Patients who have been previously treated with mTOR inhibitors such as everolimus and temsirolimus, or with c-MET inhibitors such as cabozantinib * Patients who have organ allografts * Known or suspected autoimmune disease; patients with a history of inflammatory bowel disease (including Crohn's disease and ulcerative colitis) and autoimmune disorders such as rheumatoid arthritis, systemic progressive sclerosis (scleroderma), systemic lupus erythematosus or autoimmune vasculitis (e.g., Wegener's granulomatosis) are excluded from this study; patients with a history of Hashimoto's thyroiditis only requiring hormone replacement, type I diabetes, or psoriasis not requiring systemic treatment, or conditions not expected to recur in the absence of an external trigger are allowed to participate * Known history of testing positive for human immunodeficiency virus (HIV) or known acquired immunodeficiency syndrome (AIDS) * Any underlying medical condition, which in the opinion of the investigator, will make the administration of study drug hazardous or obscure the interpretation of adverse events, such as a condition associated with frequent diarrhea, uncontrolled nausea, vomiting, malabsorption syndrome or small bowel resection that may significantly alter the absorption of MGCD516 * Patients must not have received prior anticancer therapy with any immune checkpoint inhibitors such as anti-CLTA-4, anti-PD1, or anti-PD-L1 * Patients receiving any concomitant systemic therapy for renal cell cancer are excluded * Patients must not be scheduled to receive another experimental drug while on this study * Patients who are on high dose steroid (e.g., \> 10 mg prednisone daily or equivalent) or other more potent immune suppression medications (e.g., infliximab); topical, inhaled, intra-articular, ocular, or intranasal corticosteroids (with minimal systemic absorption) are allowed; a brief course (=\< 48 hours) of systemic corticosteroids for prophylaxis (e.g., from contrast dye allergy) is permitted * Patients who have any severe and/or uncontrolled medical conditions or other conditions that could affect their participation in the study such as: symptomatic congestive heart failure of New York Heart Association class III or IV; unstable angina pectoris, symptomatic congestive heart failure, myocardial infarction within 6 months of start of study drug, serious uncontrolled cardiac arrhythmia or any other clinically significant cardiac disease; severely impaired lung function as defined as oxygen (O2) saturation that is 88% or less at rest on room air; uncontrolled diabetes as defined by blood glucose \> 200 mg/dl (11.1 mmol/l); systemic fungal, bacterial, viral, or other infection that is not controlled (defined as exhibiting ongoing signs/symptoms related to the infection and without improvement) despite appropriate antibiotics or other treatment; liver disease such as cirrhosis or chronic active hepatitis; positive test for hepatitis B virus (HBV) using HBV surface antigen (HBV sAg) test or positive test for hepatitis C virus (HCV) using HCV ribonucleic acid (RNA) or HCV antibody test indicating acute or chronic infection * Patients must not have history of other diseases, metabolic dysfunction, physical examination finding, or clinical laboratory finding giving reasonable suspicion of a disease or condition that contraindicates the use of MGCD516 or nivolumab or that might affect the interpretation of the results of the study or render the subject at high risk from treatment complications * Patients should not receive immunization with attenuated live vaccines within one week (7 days) of study entry or during study period * Uncontrolled brain or leptomeningeal metastases, including patients who continue to require glucocorticoids for brain or leptomeningeal metastases * Female patients who are pregnant or breast feeding, or adults of reproductive potential who are not using effective birth control methods; if barrier contraceptives are being used, these must be continued throughout the trial by both sexes; hormonal contraceptives are not acceptable as a sole method of contraception; (women of childbearing potential must have a negative urine or serum pregnancy test within 14 days prior to study entry; pregnancy test must be repeated if performed \> 14 days before administration of MGCD516) * Any patients who cannot be compliant with the appointments required in this protocol must not be enrolled in this study * Concurrent therapy with medications known to significantly prolong the QT interval and/or associated with increased risk for Torsade de Pointes arrhythmia; the principal investigator (PI) is the final arbiter in questions related to eligibility * Patients with left ventricular ejection fraction (LVEF) \< 40%