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)