Study of Vorinostat (MK0683), an Histone Deacetylase (HDAC) Inhibitor in Combination With Bortezomib in Patients With Relapsed or Refractory Multiple Myeloma (MK-0683-095)

Inclusion Criteria:

* Has an established diagnosis of multiple myeloma based on myeloma diagnostic criteria
* Must have adequate organ function
* Is refractory to prior bortezomib regimen and have also been exposed to prior Immunomodulatory imide drugs (IMiD: thalidimide or lenalidmide)
* Has relapsed and refractory multiple myeloma after at least 2 prior treatment regimens
* Has performance status of ≤ 2 on the Eastern Cooperative Oncology Group (ECOG) Performance Scale
* Has measurable disease, defined as any quantifiable serum monoclonal (M) protein value and, where applicable, urine light chain of ≥200 mg/24 hours
* Female participants are not pregnant and not breastfeeding, and are not a woman of childbearing potential (WOCBP) or are a WOCBP who agrees to follow contraceptive guidance during the treatment period and for at least 30 days after the last dose of study intervention
* Male participants must agree to use approved contraception during the treatment period and for at least 30 days after the last dose of study intervention and refrain from donating sperm during this period
* Is relapsed, refractory, intolerant, and/or ineligible (in the opinion of the investigator) to other therapies including an IMiD (thalidomide or lenalidomide)
* Is refractory to bortezomib (no response on prior bortezomib containing regimen or progression on or within 60 days of bortezomib containing regimen

Exclusion Criteria:

* Has known hypersensitivity to any components of bortezomib or vorinostat
* Has had a prior allogeneic bone marrow transplant or plans to undergo any type of bone marrow transplantation within 4 weeks of the initiation of study therapy
* Has an active systemic infection
* Has acute diffuse infiltrative pulmonary disease or pericardial disease
* Has known hypersensitivity to any components of bortezomib or vorinostat
* Has active Hepatitis B or C, plasma cell leukemia, or is human immunodeficiency virus (HIV) positive
* Has history of a prior malignancy with the exception of cervical intraepithelial neoplasia; non-melanoma skin cancer; adequately treated localized prostate carcinoma with prostate specific antigen (PSA) \< 0.1; or who has undergone potentially curative therapy with no evidence of that disease for five years, or who is deemed at low risk for recurrence by his/her treating physician
* Has known central nervous system (CNS) metastases and/or carcinomatous meningitis
* Has plasma cell leukemia defined as the presence of more than 20% plasma cells in the peripheral blood and an absolute plasma cell count of at least 2000/μL
* Has a history of a gastrointestinal surgery or other procedures that might, in the opinion of the Investigator, interfere with the absorption or swallowing of the study drug
* Has preexisting National Cancer Institute (NCI) Common Toxicity Criteria (CTC) Grade 1 neuropathy with pain or \>Grade 2 neuropathy