Study Assessing Activity of Molecularly Matched Targeted Therapies in Select Tumor Types Based on Genomic Alterations

Inclusion Criteria: 1. Patients with a histologically or cytologically confirmed diagnosis of one of the following tumor types whose disease has progressed following one line of standard therapy and/or for which no standard treatment is available that has been shown to prolong survival: 1. Non-small cell lung cancer 2. Urothelial carcinoma 3. Non-colon gastrointestinal cancers (including hepatobiliary, pancreatic, and gastroesophageal tumors) 4. Upper aerodigestive tract cancers (including lip, tongue, salivary gland, gum, oral cavity, mouth, tonsils, oropharynx, nasopharynx, nasal cavity, sinus, and larynx tumors) 2. Patients must have a predefined genomic alteration that can be targeted with any of the FDA-approved targeted agents used in this study. 3. Measurable disease per Response Evaluation Criteria in Solid Tumors (RECIST) v1.1 4. Eastern Cooperative Oncology Group (ECOG) Performance Status of 0 or 1. 5. Age greater than or equal to 18 years. 6. Adequate hematologic function defined as: * Absolute neutrophil count (ANC) ≥1500/μL * Platelets ≥75,000/μL 7. Adequate liver function defined as: * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 2.5 x the upper limit of normal (ULN) or ≤ 5.0 X ULN if liver metastases present * Total bilirubin ≤1.5 x ULN (unless the patient has Grade 1 bilirubin elevation due to Gilbert's disease or a similar syndrome involving slow conjugation of bilirubin) 8. Adequate renal function defined as serum creatinine ≤1.5 x the upper limit of normal OR measured or calculated creatinine clearance ≥50 mL/min for patients with creatinine levels greater than or equal to 1.5 x the upper limit of normal. 9. Patients who are therapeutically treated with an agent such as warfarin or heparin will be allowed to receive either regorafenib or afatinib provided that their medication dose and INR/PTT are stable. Close monitoring is mandatory if the patient is receiving anticoagulants. If values are above the therapeutic range the anticoagulant doses should be modified and assessments should be repeated until stable. 10. Male patients with female partners of childbearing potential and women patients of childbearing potential are required to use two forms of acceptable contraception, including one barrier method, during their participation in the study and for 90 days following last dose of study drug(s). Male patients must also refrain from donating sperm during their participation in the study and for 90 days after the last dose of study drug. 11. Willingness and ability to comply with study and follow-up procedures. 12. Ability to understand the nature of this study and give written informed consent. Exclusion Criteria: 1. Two or more prior chemotherapy regimens in the metastatic setting. 2. Most recent chemotherapy ≤ 3 weeks and \> Grade 1 chemotherapy-related side effects, with the exception of neuropathy (\> grade 2 excluded) and alopecia. 3. Use of a study drug or targeted therapy ≤21 days or 5 half-lives (whichever is shorter) prior to the first dose of study treatment. For study drugs for which 5 half-lives is ≤21 days, a minimum of 10 days between termination of the study drug and administration of study treatment is required. 4. Wide field radiotherapy (including therapeutic radioisotopes such as strontium 89) administered ≤28 days or limited field radiation for palliation ≤7 days prior to starting study drug or has not recovered from side effects of such therapy. 5. Major surgical procedures ≤28 days of beginning study drug, or minor surgical procedures ≤7 days. No waiting required following port-a-cath placement. 6. Previously untreated brain metastases. Patients who have received radiation or surgery for brain metastases are eligible if therapy was completed at least 2 weeks prior to study entry and there is no evidence of central nervous system disease progression, mild neurologic symptoms, and no requirement for chronic corticosteroid therapy. Enzyme-inducing anticonvulsants are contraindicated. 7. Pregnant or lactating 8. Acute or chronic liver, renal, or pancreas disease. 9. Presence of active gastrointestinal disease or other condition that will interfere significantly with the absorption, distribution, metabolism, or excretion of oral therapy. 10. Any of the following cardiac diseases currently or within the last 6 months: * Unstable angina pectoris * Congestive heart failure (New York Heart Association (NYHA) ≥ Grade 2 * Acute myocardial infarction * Conduction abnormality not controlled with pacemaker or medication * Significant ventricular or supraventricular arrhythmias (patients with chronic rate-controlled atrial fibrillation in the absence of other cardiac abnormalities are eligible) * Valvular disease with significant compromise in cardiac function 11. Inadequately controlled hypertension. 12. Thrombotic, embolic, venous, or arterial events, such as cerebrovascular accident (including transient ischemic attacks) deep vein thrombosis or pulmonary embolism within 6 months of start of treatment. 13. Evidence or history of bleeding diathesis or coagulopathy; any haemorrhage or bleeding event ≥ NCI CTCAE Grade 3 within 4 weeks prior to start of treatment. 14. For patients receiving cabozantinib only: Do not administer cabozantinib to patients that have high risk or at high risk for severe haemorrhage. Examples include: 1. The patient has radiographic evidence of cavitating pulmonary lesion(s). 2. The patient has tumor invading or encasing any major blood vessels. 3. The patient has had hemoptysis of ≥ 0.5 teaspoon (2.5ml) of red blood within 3 months before the first dose of study treatment. 4. The patient has experienced clinically significant GI bleeding within 6 months of the first dose of study treatment. 5. The patient has experienced any other signs indicative of pulmonary hemorrhage within 3 months of the first dose of study treatment. 15. For patients receiving cabozantinib only: Do not administer cabozantinib to patients that have high risk or at high risk of perforation or fistula: 1. The patient 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. 2. Abdominal fistula, GI perforation, bowel obstruction, or intra-abdominal abscess within 6 months before first dose. Note: Complete healing of an intra-abdominal abscess must be confirmed before first dose. 3. The patient has pre-existing fistula of head and neck area. Note: Treatment areas should be healed with no sequelae from prior radiation therapy that would predispose to fistula formation. 4. The patient has pre-existing osteonecrosis of the jaw. 16. Concomitant anticoagulation at therapeutic doses with oral anticoagulants or platelet inhibitors. \[Patients receiving cabozantinib only\] 17. Note: Low-dose aspirin for cardioprotection (per local applicable guidelines), low-dose warfarin (\< 1 mg/day), and low dose, low molecular weight heparins (LMWH) are permitted. Anticoagulation with therapeutic doses of LMWH is allowed in subjects without radiographic evidence of brain metastasis, who are on a stable dose of LMWH for at least 12 weeks before randomization, and who have had no complications from a thromboembolic event or the anticoagulation regimen.Presence of a non-healing wound, non-healing ulcer, or bone fracture. 18. Patients with phaeochromocytoma. 19. Serious active infection at the time of treatment, or another serious underlying medical condition that would impair the ability of the patient to receive protocol treatment. 20. Known diagnosis of human immunodeficiency virus, hepatitis B, or hepatitis C. 21. Presence of other active cancers unless indolent and not requiring therapy. Patients with Stage I cancer who have received definitive local treatment and are considered unlikely to recur are eligible. All patients with previously treated in situ carcinoma are eligible, as are patients with history of non-melanoma skin cancer. 22. Psychological, familial, sociological, or geographical conditions that do not permit compliance with the protocol.