This phase II trial studies how well brentuximab vedotin works in treating patients with CD30 positive (+) malignant mesothelioma that cannot be removed by surgery. Monoclonal antibodies, such as brentuximab vedotin, may interfere with the ability of tumor cells to grow and spread.

PRIMARY OBJECTIVES:

I. To assess 4-month disease control rate (DCR) in pre-treated patients with unresectable malignant pleural mesothelioma (MPM) treated with brentuximab vedotin.

SECONDARY OBJECTIVES:

I. To evaluate the response rate, progression-free and overall survival, and safety/toxicity of brentuximab vedotin in CD30+ malignant mesothelioma.

II. To prospectively evaluate the incidence of CD30+ expression in malignant mesothelioma during the screening process.

III. To determine whether CD30+ expression levels in tumor tissue correlate to response to brentuximab vedotin.

EXPLORATORY OBJECTIVES:

I. To collect archival or new tissue and blood for correlative studies. II. Next generation sequencing (NGS) will be conducted on adequate tumor tissue specimens.

III. Exploratory analysis: Bank peripheral blood at baseline for subsequent cytokine or reverse phase protein array (RPPA).

OUTLINE:

Patients receive brentuximab vedotin intravenously (IV) over 30 minutes on day 1. Courses repeat every 21 days in the absence of disease progression or unacceptable toxicity.

After completion of study treatment, patients are followed up at 30 days, 3 months, 6 months and then every 6 months thereafter.

Inclusion Criteria:

• 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performance of any study-related procedure not part of normal medical care, with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care
• Female subject is either: a. post-menopausal for at least one year before the screening visit; or b. surgically sterilized; or c. 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 and at least 6 months after the last dose of brentuximab vedotin
• Male subject, even if surgically sterilized (i.e., status postvasectomy), agrees to use an acceptable barrier method for contraception (condom with a spermicidal agent), or completely abstain from heterosexual intercourse during the entire study treatment period through 6 months after the last dose of brentuximab vedotin
• Absolute neutrophil count (ANC) > 1500/mm^3
• Platelets > 100,000/mm^3
• Hemoglobin (Hgb) > 8.5 g/dL
• Total bilirubin =< 1.5 x upper limit of normal (ULN)
• Serum glutamic-oxaloacetic transaminase (SGOT) (aspartate aminotransferase [AST]) and serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase [ALT]) < 3 x ULN; AST and/or ALT may be up to 5 X ULN if with known liver metastases (mets)
• Calculated creatinine clearance must be >= 30 mL/minute
• Eastern Cooperative Oncology Group (ECOG) performance status 0-2
• Pathologic diagnosis of malignant mesothelioma (any primary site is acceptable, any histology is acceptable)
• Have unresectable malignant mesothelioma (any histology)
• Positive CD30+ immunohistochemical expression
• Any line of prior therapy - patients may be chemo-naive or chemo-refractory (any line)
• Patients must have measurable disease by modified Response Evaluation Criteria in Solid Tumors (RECIST) or RECIST; examinations for assessment of measurable disease must have been completed within 28 days prior to registration

Exclusion Criteria:

• Radiation therapy to more than 25% of the bone marrow; whole pelvic radiation is considered to be over 25%
• Prior allogeneic bone marrow or organ transplantation
• Female subject who is pregnant or breast-feeding; confirmation that the subject is not pregnant must be established by a negative serum beta-human chorionic gonadotropin (B-hCG) pregnancy test result obtained during screening; pregnancy testing is not required for post-menopausal or surgically sterilized women
• Patient has received other investigational drugs with 14 days before enrollment
• Serious medical or psychiatric illness likely to interfere with participation in this clinical study
• No prior history of malignancy within 2 years, unless cured of a skin cancer or a stage I-III solid tumor; no prior hematologic malignancy within 3 years
• Known hypersensitivity to brentuximab vedotin components
• Persons who are incarcerated at time of enrollment (e.g., prisoners) or likely to become incarcerated during the study