Velcade and Eloxatin for Patients With Malignant Pleural or Peritoneal Mesothelioma

Inclusion Criteria: * Patients must have histologically confirmed malignant pleural or peritoneal mesothelioma epithelial, sarcomatoid, or mixed subtype, not amenable to curative treatment with surgery. Patients with pleural mesothelioma will be clinically staged using the IMIG's staging criteria (section 17.1). Note that there is no staging system for peritoneal mesothelioma and those patients will only be followed for survival. Patients may be entered based on local pathology. * Patients must have had ≤2 prior form of systemic chemotherapy. Prior intracavitary chemotherapy will be considered a prior regimen unless it was given for the purpose of pleurodesis. Immunomodulators will not be regarded as chemotherapy. Prior systemic treatment with pemetrexed plus cisplatin or carboplatin will not be a contraindication for treatment with VELCADE/ELOXATIN. * Disease status must be that of measurable disease as defined by modified SWOG criteria. Measurable disease: The presence of at least one measurable lesion. If only one lesion is present, the neoplastic nature of the disease site should be confirmed by histology. Measurable lesions: Lesions that can be accurately measured in at least one dimension with the longest diameter ≥20 mm using conventional techniques or ≥10 mm using spiral CT scans. At least one level must have one rind measurement ≥15 mm. CT (specifically spiral CT) scans and MRI are the preferred methods of measurement. Clinically detected lesions will only be considered measurable when they are superficial (e.g., skin nodules and palpable lymph nodes). For the case of skin lesions, documentation by color photography, including a ruler to estimate the size of the lesion is required. NOTE: Neither pleural effusions nor positive bone scans are considered measurable. * Patients may have undergone pleurodesis. If pleurodesis was recently performed, there must be at a minimum of a 2 week delay prior to treatment initiation. If a CT scan was done prior pleurodesis, a repeat CT scan for baseline evaluation will need to be performed prior to study entry. NOTE: For patients with clinically significant pleural effusions or ascites, consideration should be given to draining the fluid prior to initiating therapy. * Patients must have an Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2 (after any palliative measures including pleural drainage have occurred), see section 14.2. * Patients must have an estimated life expectancy of at least 12 weeks. * Patient assurance of study compliance and geographic proximity that allows for adequate follow-up. * Patients must have adequate organ function at the screening visit as defined by the following laboratory values: Absolute neutrophil count (ANC) ≥ 1.5 x 109/L, Platelet count ≥100 x 109/L Hemoglobin ≥9 g/dL. Albumin ≥ 2.5 g/dL Total Bilirubin ≤2.5 x ULN Alkaline phosphatase ≤3.0 x ULN Aspartate transaminase (AST) and alanine transaminase (ALT) ≤3.0 x ULN Creatinine ≤ 1.5 x ULN NOTE: total bilirubin, alkaline phosphatase, AST, ALT ≤5 x ULN acceptable if liver has tumor involvement * Voluntary written informed consent before performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care. * Patient must be a male or female of at least 18 years of age. * Female subjects must either post-menopausal or surgically sterilized or willing to use an acceptable method of birth control (i.e., a hormonal contraceptive, intra-uterine device, diaphragm with spermicide, condom with spermicide, or abstinence) for the duration of the study. * Male subjects must agree to use an acceptable method for contraception for the duration of the study. Exclusion Criteria: * Has active peripheral neuropathy of Grade 2 or greater intensity, as defined by the National Cancer Institute (NCI) Common Toxicity Criteria for Adverse Events (CTCAE; Version 3). * Has experienced myocardial infarction within 6 months prior to enrollment or have New York Hospital Association (NYHA) Class III or IV heart failure, uncontrolled angina, severe uncontrolled ventricular arrhythmias, or electrocardiographic evidence of acute ischemia or active conduction system abnormalities. Prior to study entry, any ECG abnormality noted should be documented by the investigator as not medically relevant. * Has been treated previously with VELCADE or ELOXATIN. * Has had prior radiation therapy to the target lesion, unless the lesion is clearly progressing and the interval between the most recent radiation therapy and enrollment is at least 4 weeks. * Has uncontrolled active systemic infection requiring therapy. * Has a history of allergic reaction attributable to compounds containing boron or mannitol or hypersensitivity reactions to drugs formulated with polysorbate 80. * Female subject is pregnant or breast-feeding. * Has had a serious concomitant systemic disorders (including oncologic emergencies) incompatible with the study (at the discretion of the investigator). * Has had a "currently active" second malignancy other than non-melanoma skin cancer or carcinoma in situ of the cervix are not to be registered. Patients who are not considered to have a "currently active" malignancy if they have completed therapy and are considered by their physician to be at less than 30% risk of relapse. * Has had any investigational agent within 4 weeks prior to enrollment into this study. * Is unwilling to employ adequate means of contraception (condoms, diaphragm, birth control pills, injections, intrauterine device, or abstinence). * Has disease which cannot be radiologically imaged. * Has a serious medical or psychiatric illness likely to interfere with participation in this clinical study.