Immunotherapy With Nivolumab and Ipilimumab Followed by Nivolumab or Nivolumab With Cabozantinib for Patients With Advanced Kidney Cancer, The PDIGREE Study

Inclusion Criteria: * STEP I REGISTRATION CRITERIA * Histologically documented renal cell carcinoma with clear cell component, including patients who have sarcomatoid or rhabdoid features * Any metastatic disease, including visceral, lymph node, other soft tissue and bone, measurable per RECIST 1.1 * Measurable disease as defined in the protocol * Must be intermediate or poor risk patient per International Metastatic Renal Cell Carcinoma Database (IMDC) criteria (1 or more of the following): Karnofsky performance status \[KPS\] \< 80, \< 1 year from diagnosis \[including initial nephrectomy\] to systemic treatment for metastatic disease, hemoglobin less than lower limit of normal \[LLN\], corrected calcium concentration greater than upper limit of normal \[ULN\], absolute neutrophil count greater than ULN, platelet count \> ULN) * Central nervous system (CNS) disease permitted, if stable and not otherwise causing symptoms or needing active treatment * Karnofsky performance status \>= 70% * No prior treatment with PD-1, PD-L1, or CTLA-4 targeting agents (including but not limited to nivolumab, pembrolizumab, pidilizumab, durvalumab, atezolizumab, tremelimumab, and ipilimumab), or any other drug or antibody specifically targeting T-cell co-stimulation or checkpoint pathways. The only exception is for prior treatment with nivolumab or other PD-1/PD-L1/CTLA-4 targeting therapy on pre- or post-operative trials, as long as \> 1 year since completion of systemic therapy * No prior previous systemic therapy for renal cell carcinoma (prior HD IL-2 \[\>28 days\]. Prior adjuvant sunitinib \>180 days since completion and prior immunotherapy as above are allowed). * No systemic cancer therapy less than 28 days prior to registration; no radiation therapy less than 14 days prior to registration. There must be a complete recovery and no ongoing complications from radiotherapy * Not pregnant and not nursing, because this study involves an agent that has known genotoxic, mutagenic and teratogenic effects. Therefore, for women of childbearing potential only, a negative serum or urine pregnancy test done =\< 14 days prior to registration is required * Age \>= 18 years * None of the following: * Active autoimmune disease requiring ongoing therapy * Ongoing acute toxicity \> grade 2 from previous treatment * History of severe allergic, anaphylactic or other hypersensitivity reactions to chimeric or humanized antibodies * Active hepatitis B/C, or active tuberculosis (purified protein derivative \[PPD\] response without active tuberculosis \[TB\] is allowed) * HIV-infected patients with detectable viral load within 6 months prior to registration. Patients on effective anti-retroviral therapy with undetectable viral load within 6 months prior to registration are eligible * Concurrent use of immunosuppressive medication including prednisone above 10 mg daily * Uncontrolled adrenal insufficiency * Uncontrolled hypertension (systolic blood pressure \[BP\] \> 150mmHg or diastolic BP \> 90mmHg) * Major surgery less than 28 days prior to registration * Any serious non-healing wound, ulcer, or bone fracture within 28 days prior to registration * Any arterial thrombotic events within 180 days prior to registration * Clinically significant hematuria, hematemesis, or hemoptysis within 12 weeks prior to registration * Cavitating pulmonary lesions or known endotracheal or endobronchial disease manifestations * Lesions encasing or invading any major blood vessels (this does not include tumor thrombus extending into/through renal vein/inferior vena cava \[IVC\]). Patients with tumor thrombus extending into/through renal vein are considered eligible * Moderate of severe hepatic impairment (child-Pugh B or C) * Any history of untreated pulmonary embolism or deep venous thrombosis (DVT) in the 180 days prior to registration. (Any asymptomatic, treated pulmonary embolism or asymptomatic, treated deep venous thrombosis \> 30 days prior to registration allowed) * Corrected QT interval calculated by the Fridericia formula (QTcF) \> 500 ms * Unstable cardiac arrhythmia within 6 months prior to registration * Any gastrointestinal (GI) bleeding =\< 180 days, hemoptysis, or other signs of pulmonary hemorrhage =\< 90 days prior to registration * History of abdominal fistula, gastrointestinal perforation, intra-abdominal abscess, bowel obstruction, or gastric outlet obstruction within 180 days prior to registration * Active peptic ulcer disease, inflammatory bowel disease, or malabsorption syndrome within 28 days prior to registration * Untreated hypothyroidism (treated hypothyroidism on thyroid replacement therapy is allowed. Abnormal thyroid-stimulating hormone \[TSH\] is acceptable with normal T3/free T4 if treated on thyroid replacement therapy) * Evidence of pancreatitis, history of organ transplant, or history of congenital QT syndrome * Active treatment with coumarin agents (e.g., warfarin), direct thrombin inhibitors (e.g., dabigatran), direct Xa inhibitor betrixaban or platelet inhibitors (e.g., clopidogrel) within 5 days of registration Allowed anticoagulants include: prophylactic use of low-dose aspirin for cardio-protection (per local applicable guidelines) and low-dose low molecular weight heparins (LMWH), therapeutic doses of LMWH or anticoagulation with direct factor Xa inhibitors rivaroxaban, edoxaban, apixaban. Allowed also in patients with known brain metastases who are on a stable dose of the anticoagulant for at least 1 week prior to registration without clinically significant hemorrhagic complications from the anticoagulation regimen or the tumor * Significant cardiac ischemia events (ST elevation myocardial infarction \[STEMI\] or non-ST-elevation myocardial infarction \[NSTEMI\]) within 6 months or active New York (NY) Heart Association class 3-4 heart failure symptoms * Absolute neutrophil count (ANC) \>= 1,500/mm\^3 * Platelet count \>= 100,000/mm\^3 * Hemoglobin \>= 8 g/dL * Calculated (Calc.) creatinine clearance \>= 30 mL/min * Urine protein =\< 1+ or urine protein to creatinine (UPC) ratio \< 1 * Total bilirubin =\< 1.5 x upper limit of normal (ULN) (except for patients with known or likely Gilbert's syndrome, for whom total bilirubin up to 3 mg/dL is allowed with direct bilirubin =\< 20% total bilirubin) * Aspartate aminotransferase/alanine aminotransferase (AST/ALT) =\< 2.5 x upper limit of normal (ULN) or \< 5 x ULN if hepatic metastases present * STEP 2 REGISTRATION ELIGIBILITY CRITERIA * Successful completion of at least 1 cycle of ipilimumab/nivolumab * Resolution of any treatment-related adverse events to grade 1 or less per dose modification section (this criteria does not include any adverse events \[AEs\] not attributable to treatment which are present due to disease), with prednisone-equivalent dosing at 10 mg daily or less. Exceptions for this criteria include patients receiving replacement hormone treatments (such as levothyroxine for treatment-related hypothyroidism or glucocorticoid replacement for adrenal insufficiency). Please contact study chair if further discussion is needed * No more than 80 days from last dose of ipilimumab/nivolumab