Tasquinimod has previously been studied as an anti-cancer agent in patients with other cancers, including a phase 3 randomized trial in patients with metastatic prostate cancer that showed an improvement in radiographic progression-free survival. The side effect profile of tasquinimod is well-characterized based on this previous experience. This trial will establish a maximum tolerated dose and optimal schedule for administration of tasquinimod in patients with multiple myeloma and then investigate the maximum tolerated dose of tasquinimod in combination with a standard myeloma regimen of ixazomib, lenalidomide, and dexamethasone (IRd). For both single agent tasquinimod and the combination of tasquinimod with IRd, exploratory expansion cohorts will be enrolled to preliminarily characterize the antimyeloma activity of each regimen.