Cabozantinib in Recurrent/Metastatic Merkel Cell Carcinoma

Inclusion Criteria: * Must have histologically or cytologically confirmed Merkel Cell Carcinoma that is metastatic or unresectable and for which standard curative measures do not exist or are no longer effective * Must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as ≥ 20 mm with conventional techniques or as ≥10 mm with spiral CT scan (see section 10 for the evaluation of measureable disease). Tumors within a previously irradiated field will be designated as "non-target" lesions unless progression is documented * Must have had one prior platinum-based chemotherapeutic regimen for management of primary disease containing carboplatin, cisplatin or another organoplatinum compound. Patients are also eligible if they received curative intent platinum-based therapy and progressed within a year of therapy * No prior MET inhibitor is allowed * At least 2 weeks since prior chemotherapy or radiation therapy. At least 3 weeks since prior biologics or investigational agents * Recovery from effects of recent treatment to baseline or CTCAE ≤ grade 1 toxicity from all prior therapies except alopecia and other non-clinically significant AEs * Participants must be ≥18 years of age * ECOG performance status ≤1 * Participants must have normal organ and marrow function * Women of child-bearing potential and men must agree to use adequate contraception prior to study entry and for the duration of study participation * Ability to understand and the willingness to sign a written informed consent document * Collection of archival tissue specimens for confirmation of Merkel Cell Carcinoma Exclusion Criteria: * Participants who have had chemotherapy or radiotherapy within 2 weeks prior to entering the study or those who have not recovered from adverse events due to agents administered more than 2 weeks earlier * Participants may not be receiving any biologics or investigational agents within 3 weeks * The subject has active brain metastases or epidural disease * History of allergic reactions attributed to compounds of similar chemical or biologic composition to cabozantinib * Has prothrombin time (PT)/ International Normalized Ratio (INR) or partial thromboplastin time (PTT) test ≥ 1.3 the institutional ULN within 7 days before the first dose of study treatment, unless PT/PTT prolongation known to be secondary to conditions not associated with increased bleeding risk (as on antiphospholipid antibody syndrome) * Requires concomitant treatment, in therapeutic doses, with anticoagulants * Active bleeding or pathologic conditions that carry high risk of bleeding * Have experienced clinically significant gastrointestinal bleeding within 6 months before first dose of study treatment * Requires chronic concomitant treatment of strong CYP3A4 inducers * Is unable or unwilling to swallow tablets * Has a corrected QT interval calculated by the Fridericia formula (QTcF)\>500 ms within 28 days before initiation of cabozantinib * Has evidence of tumor invading the GI tract or any evidence of endotracheal or endobronchial tumor within 28 days before the first dose of cabozantinib * Has radiographic evidence of cavitating pulmonary lesion(s) * Has uncontrolled, significant intercurrent or recent illness * Other disorders associated with a high risk of fistula formation including PEG tube placement within 3 months before the first dose of study therapy * History of major surgery within 3 months or minor surgery within 1 month of the first dose of cabozantinib * Pregnant women * Individuals with a history of other malignancies are eligible if they have been disease-free for at least 5 years and are deemed by the investigator to be at low risk for recurrence of that malignancy * HIV-positive individuals on combination antiretroviral therapy