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             not part of normal medical care, with the understanding that consent may be withdrawn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