Imatinib Mesylate and Bevacizumab in Treating Patients With Advanced Melanoma or Other Advanced Cancers

Inclusion Criteria: * Histologically or cytologically confirmed diagnosis of 1 of the following: * Metastatic or unresectable malignancy for which standard curative or palliative measures do not exist or are no longer effective (phase I) (phase I study closed to accrual as of 8/23/04) * Melanoma (phase I and II) * Measurable disease (phase II) * No history or clinical evidence of CNS disease, including primary brain tumor or brain metastases * Performance status - ECOG 0-1 * More than 3 months * WBC at least 3,000/mm\^3 * Absolute granulocyte count at least 1,500/mm\^3 * Platelet count at least 100,000/mm\^3 * No history of bleeding diathesis or coagulopathy * Bilirubin no greater than 1.5 times upper limit of normal (ULN) * AST and ALT no greater than 2.5 times ULN * INR no greater than 1.5 * APTT normal * Creatinine no greater than 2.0 times ULN * Creatinine clearance at least 40 mL/min * No proteinuria * Urinary protein less than 500 mg/24 hours * No history of stroke * No uncontrolled hypertension within the past 6 months * Blood pressure less than 150/100 mm Hg on a stable antihypertensive regimen * None of the following within the past 6 months: * Myocardial infarction * Unstable angina * New York Heart Association class II-IV congestive heart failure * Serious cardiac arrhythmia requiring medication * Grade II or greater peripheral vascular disease * Transient ischemic attack * Cerebrovascular accident * Other arterial thromboembolic event * Other clinically significant cardiovascular disease * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective barrier contraception during and for at least 3 months after study participation * No seizures not controlled with standard medical therapy * No prior allergic reactions attributed to Chinese hamster ovary cell products, other recombinant human antibodies, or compounds of similar chemical or biological composition to imatinib mesylate * No serious, nonhealing wound, ulcer, or bone fracture * No ongoing or active infection requiring parenteral antibiotics * No significant traumatic injury within the past 28 days * No psychiatric illness or social situation that would preclude study compliance * No other concurrent uncontrolled illness * More than 4 weeks since prior immunotherapy * More than 8 weeks since prior monoclonal antibody therapy * No concurrent prophylactic granulocyte or platelet colony-stimulating factors * More than 4 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin) * No more than 1 prior cytotoxic chemotherapy regimen for advanced disease (phase II) * More than 4 weeks since prior radiotherapy * More than 28 days since prior major surgical procedure or open biopsy * Recovered from prior therapy * No concurrent chronic daily aspirin (greater than 325 mg/day) or nonsteroidal anti-inflammatory drugs known to inhibit platelet function * No recent or concurrent full-dose anticoagulants (except as required to maintain patency of preexisting permanent indwelling IV catheters) or thrombolytic agent * No concurrent grapefruit juice * No concurrent cytochrome P450 enzyme-inducing antiepileptic drugs (e.g., phenytoin, carbamazepine, or phenobarbital) * No concurrent combination antiretroviral therapy for HIV-positive patients * No other concurrent investigational or commercial agents or therapies directed at the malignancy * No other concurrent investigational agents