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)