The goal of this clinical research study is to compare the safety and effectiveness of cabozantinib and sunitinib when given to patients with metastatic (has spread) variant histology renal cell carcinoma (vhRCC), a type of kidney cancer.

This is an investigational study. Cabozantinib and sunitinib are both FDA approved and commercially available for the treatment of advanced kidney cancer, including vhRCC.

The study doctor can explain how the study drugs are designed to work.

Up to 84 participants will be enrolled in this study. All will take part at MD Anderson.

Study Groups:

If participant is found to be eligible to take part in this study, participant will be randomly assigned (as in the flip of a coin) to 1 of 2 study groups. This is done because no one knows if one group is better, the same, or worse than the other.

• If participant is assigned to Group 1, participant will receive cabozantinib.
• If participant is assigned to Group 2, participant will receive sunitinib.

Both participant and the study doctor will know to which group participant has been assigned.

Study Drug Administration:

Each study cycle is 6 weeks.

If participant is in Group 1, participant will take cabozantinib tablets by mouth 1 time a day at about the same time every day while on study with a cup (about 8 ounces) of water. The tablets must be swallowed whole. Participant should not crush or chew them. Participant's dose of cabozantinib must be taken on an empty stomach (participant should not eat for at least 2 hours before and at least 1 hour after participant's dose).

If participant is in Group 2, participant will take sunitinib tablets by mouth 1 time a day on a "4 weeks on/2 weeks off" schedule. This means participant will take sunitinib on Days 1-28 and then participant will not take any drug between Days 29-42. Participant may take the tablets with or without food. Sunitinib tablets should be swallowed whole (participant should not crush or chew them) with at least 1 cup of water.

For all participants, if participant misses a dose, participant may take it as soon as participant remembers as long as it has been less than 12 hours of participant's scheduled dose. If it has been more than 12 hours since participant's missed dose, participant must wait until participant's next dose.

Length of Study:

Participant may continue taking the study drug for as long as the doctor thinks it is in participant's best interest. Participant may no longer be able to take the study drug if the disease gets worse, if intolerable side effects occur, or if participant is unable to follow study directions.

Participation in this study will be over after follow-up.

Study Visits:

About 7 days before participant's first dose of study drug, the following tests will be performed. If participant has had them done recently, they may not need to be repeated.

• Participant will have a physical exam.
• Participant will have an EKG.
• Blood (about 3½ teaspoons) will be drawn for routine tests and biomarker testing.
• Urine will be collected for routine tests and to check participant's kidney function.
• If participant can become pregnant, blood (about 1 teaspoon) or urine will be collected for a pregnancy test within 24 hours before participant can begin to receive the study drug(s).

On Day 1 of Week 1 every 6 weeks after that (Weeks 7, 13, 19, 25, and so on):

• Participant will have a physical exam.
• Blood (about 3½ teaspoons) will be drawn for routine and biomarker testing.

Every 6 weeks:

• Participant will have an EKG.
• Participant will have imaging scans
• Blood (about 2 teaspoons) will be drawn to check participant's thyroid function.
• If participant can become pregnant, blood (about 1 teaspoon) or urine will be collected for a pregnancy test.

End-of-Treatment:

About 30 days after participant's last dose of study drug:

• Participant will have a physical exam.
• Participant will have an EKG.
• Blood (about 2½ teaspoons) will be drawn for routine and biomarker testing.
• Urine will be collected for routine tests and to check participant's kidney function.
• If participant can become pregnant, blood (about 1 teaspoon) or urine will be collected for a pregnancy test.

If participant has a side effect at the follow-up visit and the doctor thinks it is needed, participant may be asked to continue having follow-up visits until the side effect goes away or becomes stable. This will be discussed with participant.

Long-Term Follow-up:

If participant stopped taking study drug before the disease gets worse, participant will continue to have imaging scans every 6 weeks for the first year, then every 6 months.

A member of the study staff will check up on participant to ask how participant is doing every 3 months after participant's last dose of the study drugs. This could be either a phone call or a review of participant's medical and/or other records. If participant is contacted by phone, the call should only last a few minutes.

Inclusion Criteria:

1. The subject has a histologic or cytologic diagnosis of a variant histology renal cell carcinoma including papillary, chromophobe, Xp.11 translocation, undifferentiated, or unclassified which is treatment naïve or has previously been treated with one systemic treatment line not containing any vascular endothelial growth factor antibody or vascular endothelial growth factor receptor tyrosine kinase inhibitors. The patient may have received treatment with immune checkpoint therapy including nivolumab as a single agent or nivolumab plus ipilimumab in combination. Previous treatment with mammalian target of rapamycin agents such as temsirolimus or everolimus is acceptable.
2. Measurable disease per RECIST v1.1 as determined by the investigator.
3. The subject has had an assessment of all known disease sites eg, by computerized tomography (CT) scan, magnetic resonance imaging (MRI), bone scan as appropriate, within 28 days before the first dose of cabozantinib or sunitinib.
4. The subject is >/=18 years old on the day of consent;
5. The subject has an Eastern Cooperative Oncology Group (ECOG) performance status of </=2.
6. Recovery to baseline or </= Grade 1 CTCAE v.4.0 from toxicities related to any prior treatments, unless AE(s) are clinically nonsignificant and/or stable on supportive therapy;
7. The subject has organ and marrow function and laboratory values as follows within 4 days before the first dose of cabozantinib or sunitinib: a.The ANC >/= 1500/mm^3 without colony stimulating factor support; b.White blood cell count >/= 2500/mm^3 (>/= 2.5 GI/L). c.Platelets >/=100,000/mm^3; d.Hemoglobin >/= 9 g/dL; e. Bilirubin </= 1.5 x the ULN. For subjects with known Gilbert's disease, bilirubin </= 3.0 mg/dL; f.Serum albumin >/= 2.8 g/dl g.Serum creatinine </= 2.0 X ULN or calculated creatinine clearance >/= 30 mL/min (>/= 0.5 mL/sec) using the Cockcroft-Gault equation: Males: (140 - age) x weight (kg)/(serum creatinine [mg/dL] × 72) Females: [(140 - age) x weight (kg)/(serum creatinine [mg/dL] × 72)] × 0.85 h.Alanine aminotransferase (ALT), aspartate aminotransferase (AST), and alkaline phosphatase (ALP) </= 3 X upper limit of normal (ULN). ALP </= 5 X ULN with documented bone metastases. i.Urine protein/creatinine ratio (UPCR) </= 1 mg/mg (</= 113.2 mg/mmol);
8. The subject is capable of understanding and complying with the protocol requirements and has signed the informed consent document;
9. Sexually active subjects (men and women) must agree to use medically accepted barrier methods of contraception (eg, male or female condom) during the course of the study and for 4 months after the last dose of study drug(s), even if oral contraceptives are also used. All subjects of reproductive potential must agree to use both a barrier method and a second method of birth control during the course of the study and for 4 months after the last dose of study drug(s);
10. Female subjects of childbearing potential must not be pregnant at screening. Females of childbearing potential are defined as premenopausal females capable of becoming pregnant (ie, females who have had any evidence of menses in the past 12 months, with the exception of those who had prior hysterectomy). However, women who have been amenorrheic for 12 or more months are still considered to be of childbearing potential if the amenorrhea is possibly due to prior chemotherapy, antiestrogens, low body weight, ovarian suppression or other reasons.

Exclusion Criteria:

1. The subject has a variant histology that includes renal medullary carcinoma or collecting duct renal cell carcinoma. Any clear cell component in the tumor will lead to exclusion.
2. The subject has received any previous anti-angiogenic agent. Prior treatment with cabozantinib.
3. Radiation therapy for bone metastasis within 2 weeks, any other external radiation therapy within 4 weeks before the first dose of study treatment. Systemic treatment with radionuclides within 6 weeks before the first dose of study treatment. Subjects with clinically relevant ongoing complications from prior radiation therapy are not eligible;
4. The subject has received any other type of investigational agent within 28 days before the first dose of study treatment;
5. Known brain metastases or cranial epidural disease unless adequately treated with radiotherapy and/or surgery (including radiosurgery) and stable for at least 4 weeks before the first dose of study treatment. Eligible subjects must be neurologically asymptomatic and without corticosteroid treatment at the time of the start of study treatment;
6. Concomitant anticoagulation with oral anticoagulants (eg, warfarin, direct thrombin and Factor Xa inhibitors) or platelet inhibitors (eg, clopidogrel). Allowed anticoagulants are the following: o Low-dose aspirin for cardioprotection (per local applicable guidelines) is permitted. o Low-dose low molecular weight heparins (LMWH) are permitted. Anticoagulation with therapeutic doses of LMWH is allowed in subjects without known brain metastases who are on a stable dose of LMWH for at least 6 weeks before first dose of study treatment, and who have had no clinically significant hemorrhagic complications from the anticoagulation regimen or the tumor.
7. The subject has prothrombin time (PT)/INR or partial thromboplastin time (PTT) tes>/=1.3 X the laboratory ULN within 7 days before the first dose of study treatment.
8. The subject has uncontrolled, significant intercurrent or recent illness including, but not limited to, the following conditions: Cardiovascular disorders: a.Congestive heart failure New York Heart Association Class 3 or 4, unstable angina pectoris, serious cardiac arrhythmias. b.Uncontrolled hypertension defined as sustained blood pressure (BP) > 150 mm Hg systolic or > 100 mm Hg diastolic despite optimal antihypertensive treatment. c.Stroke (including transient ischemic attack [TIA]), myocardial infarction (MI), or other ischemic event, or thromboembolic event (eg, deep venous thrombosis, pulmonary embolism) within 6 months before first dose.
9. Continuation of 8:Gastrointestinal (GI) disorders including those associated with a high risk of perforation or fistula formation: The subject has evidence of tumor invading the GI tract, active peptic ulcer disease, inflammatory bowel disease (eg, Crohn's disease), diverticulitis, cholecystitis, symptomatic cholangitis or appendicitis, acute pancreatitis, acute obstruction of the pancreatic duct or common bile duct, or gastric outlet obstruction. Abdominal fistula, GI perforation, bowel obstruction, or intra-abdominal abscess within 6 months before first dose.
10. Continuation of 8: Clinically significant hematuria, hematemesis, or hemoptysis of > 0.5 teaspoon (2.5 ml) of red blood, or other history of significant bleeding (eg, pulmonary hemorrhage) within 12 weeks before first dose. Cavitating pulmonary lesion(s) or known endotracheal or endobronchial disease manifestation. Lesions invading or encasing any major blood vessels. Other clinically significant disorders that would preclude safe study participation. Serious non-healing wound/ulcer/bone fracture. Uncompensated/symptomatic hypothyroidism. Moderate to severe hepatic impairment (Child-Pugh B or C).
11. Major surgery (eg, GI surgery, removal or biopsy of brain metastasis) within 8 weeks before first dose of study treatment. Complete wound healing from major surgery must have occurred 1 month before first dose and from minor surgery (eg, simple excision, tooth extraction) at least 10 days before first dose. Subjects with clinically relevant ongoing complications from prior surgery are not eligible.
12. Corrected QT interval calculated by the Fridericia formula (QTcF) > 500 ms per electrocardiogram (ECG) within 28 days before first dose of study treatment
13. Pregnant or lactating females.
14. Inability to swallow tablets
15. Previously identified allergy or hypersensitivity to components of the study treatment formulations.
16. Diagnosis of another malignancy within 2 years before first dose of study treatment, except for superficial skin cancers, or localized, low grade tumors deemed cured and not treated with systemic therapy. Patients with Gleason 6 (3+3) prostate cancer with previous treatment or on active surveillance may also be allowed on protocol.
17. The subject requires chronic concomitant treatment with strong CYP3A4 inducers (eg, dexamethasone, phenytoin, carbamazepine, rifampin, rifabutin, rifapentine, phenobarbital, and St. John's Wort).