The purpose of this study is to find out what effects, good and/or bad, that ganetespib and bortezomib has on you and your cancer. The investigators will determine the side effects of different dose levels of ganetespib when given alone and the effect it has on your cancer alone. The investigators will also determine the side effects of ganetespib at different dose levels when given in combination with bortezomib and the effect the combination has on your cancer. The study will measure levels of the drug in your blood and bone marrow as well.

Bortezomib is a proteasome inhibitor that is approved by the US Food and Drug Administration (FDA) that is used for the treatment of multiple myeloma. The brand name for bortezomib is Velcade®.

Ganetespib is considered "investigational" because it has not received approval from the Food and Drug Administration for general use, although it has been previously tested in humans.

Inclusion Criteria:

• Males or females, age 18 years or older.

• Diagnosis of relapsed or refractory multiple myeloma (MM) and documentation of at least 2 prior therapies which must have included bortezomib and an immunomodulatory agent; there is no maximum number of prior regimens.

• Patients with measurable disease defined as at least one of the following:

  1. Serum M-protein ≥ 0.5 g/dl (≥ 5 g/l)
  2. Urine M-protein ≥ 200 mg/24 h
  3. Serum free light-chain (FLC) assay: Involved FLC level ≥ 10 mg/dl (≥ 100 mg/l) and an abnormal serum free light chain ratio (< 0.26 or > 1.65)
  4. Measurable plasmacytoma (prior biopsy is acceptable, should be measured within 28 days of first study drug administration).

• Subject has an Eastern Cooperative Oncology Group (ECOG) ≤ 2 OR Karnofsky ≥ 60% performance status.

• Females of childbearing potential*: Confirmation that the subject is not pregnant must be established by a negative serum β-human chorionic gonadotropin (β-hCG) pregnancy test result obtained during screening. Pregnancy testing is not required for post-menopausal or surgically sterilized women. FCBP must also agree to ongoing pregnancy testing. Men must agree to use a latex condom during sexual contact with a FCBP even if they have had a successful vasectomy. *(FCBP - A female of childbearing potential is a sexually mature woman who: 1) has not undergone a hysterectomy or bilateral oophorectomy; or 2) has not been naturally postmenopausal for at least 24 consecutive months).

• Ability to understand the purpose and risks of the study and provide signed and dated informed consent and authorization to use protected health information (in accordance with national and local subject privacy regulations).

• Voluntary written informed consent before performance of any study-related procedure not part of routine medical care with the understanding that consent may be withdrawn by the subject at any time without prejudice to future medical care.

• Inclusion clinical laboratories criteria

  1. Absolute neutrophil count (ANC) ≥ 1,000 cells/dL (1.0 x 10⁹/L) (Growth factors cannot be used within 7 days of first drug administration)
  2. Platelet count ≥ 75 x 10⁹/L (platelet transfusions cannot be used within 4 days of first drug administration)
  3. Hemoglobin ≥ 8.0 g/dl
  4. Serum aspartate aminotransferase (AST) or alanine aminotransferase (ALT) ≤ 1.5 x upper limit of normal (ULN)
  5. Serum creatinine ≤ 1.5 x ULN OR creatinine clearance ≥ 50 mL/min (Cockcroft-Gault calculation)
  6. Total bilirubin ≤ 1.5 x ULN
  7. Serum calcium (corrected for serum albumin) or ionized calcium ≥ lower limit of normal (LLN) (treatment of hypercalcemia is allowed and subject may enroll if hypercalcemia returns to normal with standard treatment).

Exclusion Criteria:

• Patients who have received chemotherapy, immunomodulatory drugs (e.g., lenalidomide, thalidomide or pomalidomide), immunotherapy, radiation therapy, or any investigational drug(s) within 14 days before enrollment or who have not recovered from the side effects of the therapy to at least grade 1. Localized radiation therapy to a single site within 7 days is acceptable.
• Prior therapy with a heat shock protein 90 (HSP90) inhibitor.
• Daily requirement for corticosteroids (except for inhalational corticosteroids); prednisone ≤ 10mg/day or equivalent is permitted for other medical conditions.
• Prior peripheral stem cell transplant within 12 weeks of the first dose of study treatment.
• Use of venous access devices made of materials other than silicone for the infusion of ganetespib. Patients with these devices are eligible as long as the device is not used for the infusion.
• History of severe allergic or hypersensitivity reactions to excipients (e.g., Polyethylene glycol [PEG] 300 and Polysorbate 80).
• Baseline corrected QT interval (QTc) > 470 msec or previous history of QT prolongation while taking other medications.
• Ventricular ejection fraction (Ef) ≤ 50 % at baseline.
• History of documented congestive heart failure (CHF), New York Heart Association class II/III/IV, with a history of dyspnea, orthopnea or edema that requires current treatment with angiotensin converting enzyme inhibitors, angiotensin II receptor blockers, beta-blockers or diuretics. NOTE: Use of these medications for the treatment of hypertension is allowed.
• High-risk uncontrolled arrhythmias (ventricular tachycardia, high-grade atrioventricular [AV]-block, supra-ventricular arrhythmias which are not adequately rate-controlled) that require current treatment with the following anti-arrythmic drugs: flecainide, moricizine or propafenone.
• History of active current coronary artery disease or unstable angina.
• Peripheral neuropathy ≥ grade 2.
• Treatment with chronic immunosuppressants (e.g., cyclosporine following transplantation).
• Uncontrolled intercurrent illness including, but not limited to, human immunodeficiency virus (HIV)-positive subjects receiving combination antiretroviral therapy, severe or systemic infection, or psychiatric illness/social situations that would limit compliance with study requirements.
• Other medications, or severe acute/chronic medical or psychiatric condition, or laboratory abnormality that may increase the risk associated with study participation or study drug administration, or may interfere with the interpretation of study results, and in the judgment of the investigator would make the subject inappropriate for entry into this study.