Sitravatinib and Nivolumab for the Treatment of Metastatic or Advanced Clear Cell Renal Cell 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 lines of treatment in the advanced or metastatic setting, and the most recent treatment must include a PD-1 or PD-L1 CPI, cabozantinib, or lenvatinib. Examples of acceptable prior regimens include: nivolumab plus ipilimumab (cohort A), pembrolizumab plus axitinib, avelumab plus axitinib, or VEGF-targeted monotherapy followed by nivolumab monotherapy (cohort B), or cabozantinib or lenvatinib with or without everolimus, received alone sequentially before PD-1/PD-L1 inhibitors, or in combination with CPIs (cohort C) * There must be evidence of progression on or after treatment (at any point after completing prior therapy) with a PD-1/PD-L1-containing regimen as the last treatment received 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 * Age \>= 18 years * Hemoglobin \>= 9 g/dl (treatment allowed) * May receive transfusion * Absolute neutrophil count \>= 1,000/uL * Platelets \>= 75,000/uL * Total bilirubin =\< 1.5 mg/dL * For patients with Gilbert's disease, total bilirubin should =\< 3 mg/dL (=\< 51.3 umol/L) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) or alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) =\< 2.5 X institutional upper limit of normal (ULN), except in known hepatic metastasis, wherein may be \< 5 x ULN * Serum Creatinine =\< 1.5 x ULN (as long as patient does not require dialysis) * 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 * Institutional normalized ratio (INR) and partial thromboplastin time (PTT) =\< 1.5 x ULN prior to study entry. Therapeutic anticoagulation is permitted if: on a stable dose of low molecular weight heparin (LMWH) for \> 2 weeks (14 days) at the time of enrollment or on a direct oral anticoagulant (DOAC) for \> 2 weeks at 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 \[HCG\]) 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, 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 sitravatinib are eligible * Patients who had a major surgery or significant traumatic injury (injury requiring \> 28 days to heal) within 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 with a prior history of grade 3 or worse immune-related adverse events attributed to CPIs (PD-1, PD-L1, or CTLA-4), except endocrine adverse events with appropriate hormone replacement or asymptomatic amylase/lipase elevations * Active or prior documented autoimmune disease, as follows: * Inflammatory bowel disease (eg, Crohn's disease, ulcerative colitis) * Interstitial lung disease (ILD), drug-induced ILD, radiation pneumonitis that required steroid treatment, or any evidence of clinically active ILD. * Other medically important autoimmune disease within 2 years before first dose of study treatment. Note: Patients with type 1 diabetes, vitiligo, Graves' disease requiring only hormone replacement, residual hypothyroidism requiring only hormone replacement, or psoriasis or Sjogren's syndrome not requiring systemic treatment are permitted * Immunocompromising conditions, as follows: * Known acute or chronic human immunodeficiency virus (HIV) infection * History of primary immunodeficiency * History or allogeneic transplant * Current or prior use of immunosuppressive medication within 28 days before the first dose of study treatment, with the exception of topical, ocular, intranasal, and inhaled corticosteroids, or systemic corticosteroids at an equivalent dose =\< 10 mg of prednisone daily * 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 sitravatinib * 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 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 02 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 sitravatinib 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 a patient can become pregnant or father a child, appropriate birth control methods, including a double-barrier method (2 methods at the same time), are required while on study and for 23 weeks (females) or 31 weeks (males) after you stop receiving the study drugs. 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 sitravatinib) * 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