Cabozantinib Plus Docetaxel and Prednisone for Advanced Prostate Cancer

* INCLUSION CRITERIA: * Must have metastatic, progressive, castrate resistant prostate cancer (CRPC). There must be radiographic evidence of disease after primary treatment with surgery or radiotherapy that has continued to progress radiographically or biochemically (rising PSA levels on successive measurements) despite adequate androgen-deprivation therapy, which is defined as having undergone bilateral surgical castration or continued treatment on GnRH agonists or antagonists. Progression must be evidenced and documented by any of the following parameters: * Two consecutively rising PSA values, above the baseline, at a minimum of 1- week intervals * Appearance of one or more new lesions on bone scan * Progressive measurable disease by RECIST 1.1 The use of androgen receptor inhibitors is not required prior to study entry. For those patients receiving an anti-androgen agent (flutamide, bicalutamide, or nilutamide), for at least 6 consecutive months immediately prior to study entry, and are entering the trial due to a rise in PSA, they must demonstrate a continued rise in PSA within 4 weeks after stopping flutamide and within 6 weeks after stopping bicalutamide or nilutamide. Flutamide, nilutamide and bicalutamide disease progression requirements only apply to patients who have been on these drugs for at least the prior 6 months. * Histopathological confirmation of prostate cancer by the Laboratory of Pathology of the National Cancer Institute (NCI) Pathology Department of the Walter Reed National Military Medical Center or YALE is required prior to entering this study. Patients whose pathology specimens are no longer available may be enrolled if the patient has a clinical course that is consistent with prostate cancer and available documentation from an outside pathology laboratory of the diagnosis. All efforts should be made to have the material forwarded to the research team for use in correlative studies in cases where original tissue blocks or archival biopsy material is available. * Patients must have metastatic disease, defined as at least one lesion on bone scan or at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded for non-nodal lesions and short axis for nodal lesions) as greater than or equal to 20 mm with conventional techniques or as greater than or equal to 10 mm with spiral computed tomography (CT) scan, magnetic resonance imaging (MRI), or calipers by clinical exam. * Patients must have a performance status of 0 to 2 according to the ECOG criteria. * Patients must have adequate bone marrow, hepatic, and renal function with: * Hemoglobin greater than or equal to 9 grams per deciliter * Leukocytes greater than or equal to 3000 per microliters * ANC greater than or equal to 1500 per microliters, without CSF support * Platelets greater than or equal to 100,000 per microliters * AST (SGOT) less than or equal to 2.5 times upper limit of normal (ULN) * ALT (SGPT) less than or equal to 2.5 times upper limit of normal (ULN) * Total serum bilirubin less than or equal to the upper limit of normal (ULN) * Serum albumin greater than or equal to 2.8 grams per deciliters * Serum phosphorus, calcium, magnesium, and potassium greater than or equal to LLN * Lipase less than 2.0 times the upper limit of normal and no radiologic or clinical evidence of pancreatitis * Creatinine less than or equal to 1.5 times institutional upper limits of normal OR * creatinine clearance of greater than or equal to 50 ml/min/1.73 m\^2 for patients with creatinine levels above institutional normal by 24 hour urine. * urine protein/urine creatinine ratio (UPCR) less than or equal to 1 * Patients must be at least 18 years of age. Because no dosing or adverse event data are currently available on the use of cabozantinib in combination with docetaxel and prednisone in patients less than 18 years of age, children are excluded from this study, but may be eligible for future pediatric trials * Patient must be capable of understanding and complying with protocol requirements and is willing to give informed consent * Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of XL184 administration. Sexually active subjects and their female partners 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 also 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). Should a woman become pregnant or suspect she is pregnant while her partner is participating in this study, she should inform her treating physician immediately. * Patients enrolled on the randomized portion of the study must have had disease progression on arbiraterone or enzalutamide. EXCLUSION CRITERIA: * The subject has had evidence within 2 years of the start of study treatment of another malignancy which required systemic treatment * The subject is unable to swallow tablets * The subject has tumor invading (or there is concern for invasion of) major blood vessel * The subject has active brain metastases or epidural disease Subjects with brain metastases previously treated with whole brain radiation or radiosurgery or subjects with epidural disease previously treated with radiation or surgery who are asymptomatic and do not require steroid treatment for at least 2 weeks before starting study treatment are eligible. Neurosurgical resection of brain metastases or brain biopsy is permitted if completed at least 3 months before starting study treatment. Baseline brain scans are not required to confirm eligibility. * The subject requires concomitant treatment, in therapeutic doses, with anticoagulants such as warfarin or warfarin-related agents, heparin, thrombin or Factor Xa inhibitors, or antiplatelet agents (e.g., clopidogrel). Low dose aspirin (less than or equal to 81 milligrams per day), low-dose warfarin (less than or equal to1 milligrams per day), and prophylactic low molecular weight heparin (LMWH) are permitted. * The subject has a corrected QT interval calculated by the Fridericia formula (QTcF) greater than 500 milliseconds within 28 days before initiation of protocol therapy. Note: if initial QTcF is found to be greater than 500 milliseconds, two additional EKGs separated by at least 3 minutes should be performed. If the average of these three consecutive results for QTcF is less than or equal to 500 milliseconds, the subject meets eligibility in this regard. * Patients with contraindication to steroid use * Prior treatment with cabozantinib * The patient has received cytotoxic chemotherapy (including investigational cytotoxic chemotherapy) or biologic agents (e.g., cytokines or antibodies) within 3 weeks, or nitrosoureas or mitomycin within 6 weeks before the first dose of study treatment. * The subject has received prior treatment with a small molecule kinase inhibitor or a hormonal therapy (including investigational kinase inhibitors or hormones) within 14 days or five half-lives of the compound or active metabolites, whichever is longer, before the first dose of study treatment with the exception of patients receiving prior abiraterone or ketoconazole. For patients receiving prior abiraterone or ketoconazole, they must discontinue the medication within 5 half lives of the compound before the first dose of study treatment in order to participate in this study. Note: Subjects with prostate cancer currently receiving LHRH or GnRH agonists must be maintained on these agents. * The subject has received any other type of investigational agent within 28 days before the first dose of study treatment. * The subject has received radiation therapy: * to the thoracic cavity or gastrointestinal tract within 3 months before the first dose of study treatment * to bone or brain metastasis within 14 days before the first dose of study treatment * to any other site(s) within 28 days before the first dose of study treatment * The subject has received radionuclide treatment within 6 weeks prior to the first dose of the study treatment * The subject has not recovered to baseline or CTCAE less than or equal to Grade 1 from toxicity due to all prior therapies, including surgery, except alopecia and other non-clinically significant AEs. * The subject has prothrombin time (PT)/ International Normalized Ratio (INR) or partial thromboplastin time (PTT) test results at screening greater than or equal 1.3 times the laboratory ULN within 7 days before the first dose of study treatment * The subject has experienced any of the following: * clinically-significant hematemesis or gastrointestinal bleeding within 6 months before the first dose of study treatment * hemoptysis of greater than or equal to 0.5 teaspoon (2.5 mL) of red blood within 3 months before the first dose of study treatment * any other signs indicative of pulmonary hemorrhage within 3 months before the first dose of study treatment * The subject has evidence of tumor invading the GI tract (esophagus, stomach, small or large bowel, rectum or anus), or any evidence of endotracheal or endobronchial tumor within 28 days before the first dose of cabozantinib * The subject has uncontrolled, significant intercurrent or recent illness including, but not limited to, the following conditions: * Cardiovascular disorders including * Congestive heart failure (CHF): New York Heart Association (NYHA) Class III (moderate) or Class IV (severe) at the time of screening * Concurrent uncontrolled hypertension defined as sustained BP greater than 140 millimeters of mercury systolic, or greater than 90 millimeters of mercury diastolic despite optimal antihypertensive treatment (BP must be controlled at screening) * Any history of congenital long QT syndrome * Any of the following within 6 months before the first dose of study treatment: * unstable angina pectoris * clinically-significant cardiac arrhythmias * stroke (including TIA, or other ischemic event) * myocardial infarction * thromboembolic event requiring therapeutic anticoagulation (Note: subjects with a venous filter (e.g. vena cava filter) are not eligible for this study) * Gastrointestinal disorders particularly those associated with a high risk of perforation or fistula formation including: * Any of the following within 28 days before the first dose of study treatment * intra-abdominal tumor/metastases invading GI mucosa * active peptic ulcer disease * inflammatory bowel disease (including ulcerative colitis and Crohns disease), diverticulitis, cholecystitis, symptomatic cholangitis or appendicitis * malabsorption syndrome * Any of the following within 6 months before the first dose of study treatment: * history of abdominal fistula * gastrointestinal perforation * bowel obstruction or gastric outlet obstruction * intra-abdominal abscess. Note: Complete resolution of an intra-abdominal abscess must be confirmed prior to initiating treatment with cabozantinib even if the abscess occurred more than 6 months ago. * Other disorders associated with a high risk of fistula formation including PEG tube placement within 3 months before the first dose of study therapy or concurrent evidence of intraluminal tumor involving the trachea and esophagus. * Other clinically significant disorders such as: * active infection requiring intravenous treatment within 10 days of starting protocol * serious non-healing wound/ulcer/bone fracture within 28 days before the first dose of study treatment * history of organ transplant * concurrent uncompensated hypothyroidism or thyroid dysfunction within 7 days before the first dose of study treatment * history of major surgery as follows: * Major surgery within 3 months of the first dose of cabozantinib if there were no wound healing complications or within 6 months of the first dose of cabozantinib if there were wound complications * Minor surgery within 1 months of the first dose of cabozantinib if therewere no wound healing complications or within 3 months of the first dose of cabozantinib if there were wound complications. In addition, complete wound healing from prior surgery must be confirmed at least 28 days before the first dose of cabozantinib irrespective of the time from surgery * HIV-positive patients on combination antiretroviral therapy are ineligible because of the potential for pharmacokinetic interactions with the study agents. In addition, these patients are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in patients receiving combination antiretroviral therapy when indicated. * Patients who require taking drugs that are strong inhibitors/inducers of CYP3A4 and cannot be switched to an alternative medication. Because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated list such as http://medicine.iupui.edu/clinpharm/ddis/; medical reference texts such as the Physicians' Desk Reference may also provide this information. As part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-thecounter medicine or herbal product. * Patients with greater than or equal to grade 2 peripheral neuropathy at baseline. * The subject has had treatment with docetaxel for the treatment of metastatic castratesensitive prostate cancer within 6 months before the first dose of study treatment. * The subject has had progression of prostate cancer during 6 cycles of prior docetaxel treatment for castrate sensitive disease. * The subject has received chemotherapy for castration-resistant prostate cancer.