Vorinostat, Bortezomib and Dexamethasone in Multiple Myeloma (MUKFour)

Inclusion Criteria: * Able to give informed consent - Aged 18 years or over * Participants with relapsed myeloma who have received 1-3 prior lines of treatment and now require further treatment * ECOG Performance Status ≤ 2 * Required laboratory values within 14 days of registration: * Absolute neutrophil count ≥1.0 x 10\^9/L. * Platelet count ≥75x10\^9/L. * Haemoglobin \> 9 g/dL. * Bilirubin ≤1.5 x upper limit of normal * ALT and / or AST ≤2.5 x upper limit of normal * Serum creatinine ≤ 2.0 x upper limit of normal * Corrected calcium ≤ 2.8 mmol/L * Life expectancy of at least 3 months * Female participants of child-bearing potential must have a negative pregnancy test at baseline and agree to use dual methods of contraception for the duration of the study and must continue to do so for 3 months after the end of treatment. Male participants must agree to use a barrier method of contraception for the duration of the study if sexually active with a female of child-bearing potential and must continue to do so for 3 months after the end of treatment * Participant is able to swallow capsules and is able to take or tolerate oral medications on a continuous basis. Exclusion Criteria: * Previous anti-tumour therapies, including prior experimental agents or approved anti-tumour small molecules and biologics, within 28 days before the start of protocol treatment. Steroid therapy to stop rapid relapse during this period is permitted, but must be stopped 7 days prior to study drug administration. * Prior HDAC inhibitor treatment. * Previous or concurrent active malignancies (\<12 months post end of treatment) at other sites with the exception of appropriately treated localised epithelial skin or cervical cancer. * Participants considered to be refractory to prior bortezomib treatment or unable to tolerate treatment with bortezomib. * Peripheral neuropathy of ≥ grade 2 severity * Participants who have received growth factor support or platelet support within 14 days prior to registration * Participants with uncontrolled concurrent illness or circumstances that could limit compliance with the study. * Patients with significant cardiovascular or pulmonary disease * Active symptomatic fungal, bacterial, and/or viral infection including known active HIV or known viral (A, B, or C) hepatitis. * Pregnant or breast feeding females * Unable to take corticosteroid therapy at study entry * Participants with known hypersensitivity to any components of bortezomib, (such as boron, mannitol), vorinostat or dexamethasone. * Participant has known CNS metastases and/or carcinomatous meningitis. * Participants with 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(s)