Sorafenib and Bortezomib in Treating Patients With Advanced Cancer

Inclusion Criteria: * Diagnosis of 1 of the following: * Cytologically or histologically proven unresectable solid tumor for which no curative treatment options exist (group I - dose-escalation phase) * Multiple myeloma or chronic lymphocytic leukemia requiring treatment (group II - maximum tolerated dose phase) * Failed ≥ 1 prior regimen * Non-secretory myeloma allowed * No known standard therapy that is potentially curative or definitely capable of extending life expectancy exists * Tumor amenable to serial sampling (group II) * ECOG performance status 0-2 * Absolute neutrophil count ≥ 1,500/mm\^3 * Hemoglobin ≥ 9 g/dL * Platelet count ≥ 100,000/mm\^3 (75,000/mm\^3 for patients with multiple myeloma \[group II\]) * Bilirubin ≤ 1.5 times upper limit of normal (ULN) * AST ≤ 3 times ULN (5 times ULN if liver involvement) * Creatinine ≤ 1.5 times ULN (2.5 times ULN for patients with multiple myeloma \[group II\]) * Life expectancy ≥ 12 weeks * No uncontrolled infection * No New York Heart Association class III or IV heart disease * No uncontrolled hypertension, labile hypertension, or history of poor compliance with antihypertensive medication * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No sensory peripheral neuropathy of any etiology \> grade 1 or neuropathic pain of any etiology * No active HIV infection requiring therapy * No inability to swallow that would preclude use of oral medications * No evidence of bleeding diathesis * Medically capable and willing to provide biologic specimens as required (mandatory for patients in group II) * Priorbortezomib allowed * More than 3 weeks since prior chemotherapy (6 weeks for mitomycin C or nitrosoureas) and recovered * More than 4 weeks since prior immunotherapy or biologic therapy * More than 2 weeks since prior steroid therapy (group II only) * No prior anti-vascular endothelial growth factor therapy * More than 4 weeks since prior full-field radiotherapy (2 weeks for limited-field radiotherapy) * No prior radiation to \> 25% of bone marrow * More than 4 weeks since major surgery (e.g., laparotomy) (2 weeks for minor surgery) * Insertion of a vascular access device is not considered major or minor surgery * No concurrent chemotherapy, immunotherapy, radiotherapy, or any ancillary other therapy considered investigational * No concurrent prophylactic colony-stimulating factors * No concurrent therapeutic anticoagulation * Concurrent prophylactic anticoagulation (i.e., low-dose warfarin) of venous or arterial access devices allowed provided requirements for PT, INR, or PTT are met * No concurrent cytochrome P450 enzyme-inducing antiepileptic drugs (e.g., phenytoin, carbamazepine, and phenobarbital), rifampin, or Hypericum perforatum (St. John's Wort) * No concurrent participation in any other study involving a pharmacologic agent (e.g., drugs, biologics, immunotherapy, or gene therapy), either for symptom control, or therapeutic intent