This study will evaluate GMI-1271, a specific E-selectin antagonist, in multiple myeloma as adjunct to standard of care chemotherapy used to treat this disease.

Inclusion Criteria:

1. Males and females ≥ 18 years of age
2. Confirmed diagnosis of Multiple Myeloma
3. Subjects with progressive MM who have received at least 1 prior therapy and who have already undergone or are not expected to undergo hematopoietic stem cell transplantation
4. Subjects previously treated with an IMiD-based regimen or ineligible for an IMiD-based treatment regimen
5. Subjects must be receiving treatment with a proteasome inhibitor-based regimen (bortezomib-based or carfilzomib-based)
6. Adequate hepatic, renal, and cardiac function

Exclusion Criteria:

1. Intolerant to bortezomib or carfilzomib
2. Progressing evidence of end organ damage attributed to the underlying disease
3. Plasma cell leukemia
4. Congestive heart failure
5. Acute active infection
6. Non-hematologic malignancy within the past 3 years except: a) adequately treated basal cell or squamous cell skin cancer, b) carcinoma in situ of the cervix, or c) prostate cancer with stable PSA
7. Significant peripheral neuropathy