Inclusion Criteria:

- Patients must have histologically or cytologically confirmed stage IIa or IIIa
multiple myeloma

- Patient has progressive disease and has had 1, 2, 3, or 4 prior lines of therapy

- Bilirubin < 2.0 mg/dL

- SGOT/SGPT =< 2.5 X institutional upper limit of normal

- Serum creatinine =< 1.5 mg/dl OR creatinine clearance >= 60 mL/min/1.73 m^2 for
patients with creatinine levels above institutional normal

- Karnofsky Performance Status equal or greater than 70%; KPS 60% will be allowed if
reduced KPS is due to advanced skeletal disease

- Measurable disease as defined by serum M protein >= 1.0 gm/dl measured by serum
protein electrophoresis or free light chain measurement, or quantitative
immunoglobulins and/or urinary M protein excretion >= 200 mg/24 hrs

- Ejection fraction >= 50% and normal baseline EKG tracing

- No known central nervous system abnormality including neoplastic, vascular,
inflammatory, degenerative or epilepsy

- Life expectancy of greater than 12 weeks

- Leukocytes >= 3,000/uL

- Absolute neutrophil count >= 1,500/uL

- Platelets >= 100,000/uL

- Patients in whom cytopenias are considered to be due to myeloma marrow infiltration
will be allowed as long as they meet the following criteria:

- Bone marrow biopsy displaying >= normal cellularity for age and >= 50%
involvement by myeloma

- ANC > 1,000 and platelets > 50,000

- Women of child-bearing potential and men must agree to use adequate contraception
(hormonal or barrier method of birth control; abstinence) prior to study entry and
for the duration of study participation; should a woman become pregnant or suspect
she is pregnant while participating in this study, she should inform her treating
physician immediately

- Ability to understand and the willingness to sign written informed consent

Exclusion Criteria:

- Administration of chemotherapy or radiotherapy within 4 weeks (6 weeks for
nitrosoureas or mitomycin C) prior to enrollment or unresolved adverse events due to
agents administered more than 4 weeks earlier

- Prior treatment with a histone deacetylase inhibitor

- Patients may not be receiving any other investigational agent

- History of second cancer (except for adequately treated basal cell or squamous cell
skin cancer, in situ cervical cancer, or other cancer for which the patient has been
disease free >= 5 years)

- Non secretory disease or plasma cell leukemia (> 2000 circulating plasma cells/uL)

- History of allergic reactions attributed to compounds of similar chemical or biologic
composition to depsipeptide

- Uncontrolled intercurrent illness including, but not limited to, ongoing or active
infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac
arrhythmia, or psychiatric illness/social situations that would limit compliance with
study requirements

- Patients with left ventricular hypertrophy or history of arrhythmias including atrial
fibrillation, myocardial infarction or congestive heart failure; patients may not be
taking hydrochlorothiazides

- Patients that are pregnant or lactating will be excluded from this trial

- Known HIV positivity; patients infected with the HIV virus will be excluded from this
trial