Immunotherapy with or without Kidney Surgery for Kidney Cancer

Inclusion Criteria: * STEP 1 REGISTRATION: Participants must have a histologically proven diagnosis of clear cell or non-clear cell renal cell carcinoma. Participants with collecting duct carcinoma histology are not eligible. Participants with multifocal or bilateral tumors are eligible * STEP 1 REGISTRATION: Participants must have primary tumor in place * STEP 1 REGISTRATION: Participants must have the following scans performed, showing clinical evidence of measurable or non-measurable metastatic disease: * Computed tomography (CT) scan of the chest (can be performed without contrast if CT contrast cannot be given) * CT of abdomen and pelvis with contrast OR magnetic resonance imaging (MRI) of the abdomen and pelvis with or without contrast Scans must be performed within the following timeframes: * Treatment naive participants must have scans documenting metastatic disease completed within 90 days prior to study registration * Previously treated participants must have scans documenting metastatic disease completed within 90 days prior to first dose of systemic treatment * STEP 1 REGISTRATION: Participants with symptomatic metastases may have received palliative radiotherapy or receive palliative radiotherapy after registration * STEP 1 REGISTRATION: Participants must have no clear contraindications to nephrectomy * STEP 1 REGISTRATION: Participants must be offered the opportunity to participate in specimen bank. With participant consent, specimens must be collected and submitted via the Southwest Oncology Group (SWOG) Specimen Tracking System * STEP 1 REGISTRATION: Participants must be informed of the investigational nature of this study and must sign and give informed consent in accordance with institutional and federal guidelines * STEP 1 REGISTRATION: As part of the Oncology Patient Enrollment Network (OPEN) registration process the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system * STEP 2 REGISTRATION: Participants must have at least one of the following scans performed 12 weeks (+/- 2 weeks) after starting pre-randomization treatment * CT scan of the chest (can be performed without contrast if CT contrast cannot be given) * CT of abdomen and pelvis with contrast OR MRI of the abdomen and pelvis with or without contrast Scans must be performed within 28 days prior to randomization. Response should be assessed by comparing with a CT or MRI of the chest, abdomen and pelvis obtained prior to starting pre-randomization treatment. Participants with complete response in all metastatic sites are not eligible to randomize to Step 2 • STEP 2 REGISTRATION: Participants must have one of the following objective statuses after 12 weeks of pre-randomization treatment * Stable disease * Partial response * The treating investigator believes the patient is deriving clinical benefit from systemic therapy AND have Zubrod performance status 0-1 * STEP 2 REGISTRATION: Participants must plan to continue the immune-based therapy received during pre-randomization treatment * STEP 2 REGISTRATION: Participants must be randomized on or between the 11th and 14th week of protocol-directed pre-randomization treatment therapy * STEP 2 REGISTRATION: Participants must have received at least one of the minimum amounts of immunotherapy: * 2 infusions of nivolumab + 1 infusion of ipilimumab * 2 infusions of pembrolizumab * 2 infusions of avelumab * STEP 2 REGISTRATION: Participants must have a planned surgery date within 42 days of randomization * STEP 2 REGISTRATION: Participants must be a surgical candidate as determined by study urologist. The urology consult should be done within 42 days prior to randomization * STEP 2 REGISTRATION: Participants must have a complete physical examination and medical history within 28 days prior to randomization * STEP 2 REGISTRATION: Participants must have a Zubrod performance status of 0-1 within 28 days prior to randomization * STEP 2 REGISTRATION: Total bilirubin =\< institutional upper limit of normal (ULN) (within 28 days prior to randomization) * STEP 2 REGISTRATION: Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 3 x institutional upper limit of normal (ULN) (within 28 days prior to randomization) * STEP 2 REGISTRATION: Serum creatinine =\< 1.5 x the institutional upper limit of normal (IULN) OR measured OR calculated creatinine clearance \>= 50 mL/min using the Cockcroft-Gault Formula) (must have been drawn and processed within 28 days prior to randomization) Exclusion Criteria: * STEP 1 REGISTRATION: Participants must not have known active brain metastases. Participants with previously treated brain metastases are eligible if participant has no neurologic signs or symptoms suggestive of brain metastasis. Brain imaging studies are not required. If brain imaging studies are performed, they must be negative for disease * STEP 1 REGISTRATION: Participants must not have received the following prior treatment of metastatic renal cell carcinoma: * Treatment naive participants must not have received any prior lines of systemic therapy for metastatic renal cell carcinoma beyond the line intended as part of protocol therapy * Previously treated participants must not have received any systemic therapy for metastatic renal cell carcinoma beyond the one regimen received off protocol as specified in Step 1 pre-randomization treatment * STEP 1 REGISTRATION: Participants must not have received more than the following amounts protocol-directed pre-randomization treatment: * Treatment naive participants must not have received any pre-randomization treatment. * Previously treated participants must not be planning to receive any additional treatment prior to Step 2 randomization, and must not have received more than the following amounts of pre-randomization treatment: * 4 infusions of nivolumab * 4 infusions of ipilimumab * 4 infusions of pembrolizumab * 7 infusions of avelumab * STEP 1 REGISTRATION: Participants must not have received immunotherapy for any cancer within the following timeframes: * Treatment naive participants must not have received any immunotherapy within a year of registration * Previously treated participants must not have received any other immunotherapy within a year of the start of off protocol specified pre-randomization treatment * STEP 1 REGISTRATION: Participants must not have a solitary kidney and not have a transplanted kidney * STEP 1 REGISTRATION: No other prior malignancy is allowed except for the following: adequately treated basal cell or squamous cell skin cancer, any in situ or T1 cancer, adequately treated stage I or II cancer from which the participant is currently in complete remission, or any other cancer from which the participant has been disease free for at least two years * STEP 1 REGISTRATION: Participants must not have been previously diagnosed with a medical condition that makes them ineligible for immune based combination therapy or nephrectomy * STEP 2 REGISTRATION: Participants must not show progression in the primary tumor. Participants who are considered to have pseudo progression are allowed * STEP 2 REGISTRATION: Participants must not have known active brain metastases. Participants with previously treated brain metastases are eligible if participant has no neurologic signs or symptoms suggestive of brain metastasis. Brain imaging studies are not required. If brain imaging studies are performed, they must be negative for disease * STEP 2 REGISTRATION: No other prior malignancy is allowed except for the following: adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, adequately treated stage I or II cancer from which the participant is currently in complete remission, or any other cancer from which the participant has been disease free for two years