This is a Phase Ib/II safety and efficacy trial of single agent ABC294640, an inhibitor of sphingosine kinase 2 and dihydroceramide desaturase, in refractory or relapsed multiple myeloma (MM). Cohorts of patients with refractory or relapsed MM who have previously been treated with proteasome inhibitors and immunomodulatory agents will receive increasing doses of oral ABC294640. The starting dosage for ABC294640 will be 250 mg bis in die (BID) which is known to be safely tolerated as a single agent, and the ABC294640 dose will be escalated to two additional dose cohorts of 500 and 750 mg BID using Bayesian model average continual reassessment method (BMA-CRM) for dose finding. It is expected that 18 patients will be used to determine the maximum tolerated dose (MTD) for ABC294640 in refractory or relapsed MM. Up to 56 additional patients will be treated on the phase II portion of the study at the MTD or maximum dose used in phase I, with interim stopping rules for futility.