Inclusion Criteria:

1. Signed informed consent
2. 18 years of age or older
3. Multiple myeloma (MM) diagnosed according to IMWG criteria
4. Measurable disease (this is defined differently in different arms)
5. Multiple myeloma relapsed or refractory to treatment (this is defined differently in different arms)
6. Meet certain clinical laboratory criteria
7. ECOG performance status ≤2
8. Life expectancy of at least 3 months
9. For women of childbearing potential, a negative serum or urine pregnancy test prior to study treatment.
10. For women who are not postmenopausal (12 months of amenorrhea) or surgically sterile (absence of ovaries and/or uterus): agreement to use two methods of contraception one of which must be highly effective
11. For men: agreement to use a barrier method of contraception for 1 month before start of study treatment, during the treatment period and for 6 months after the last dose of study treatment.

Exclusion Criteria:

1. Failure to have fully recovered (i.e. ≤ Grade 1 toxicity) from the effects of prior chemotherapy (except for alopecia)
2. Active graft versus host disease
3. Treatment with any of the following:
   1. Cytotoxic chemotherapy within 3 weeks prior to the initiation of study treatment
   2. Proteasome inhibitors, Imids, or monoclonal antibodies within 2 weeks prior to the initiation of study treatment
   3. Experimental therapy within 4 weeks or 5 half-lives, whichever is shorter
   4. Systemic corticosteroids >=10 mg prednisone or equivalent within 7 days prior to the initiation of study treatment
   5. Radiotherapy within 7 days prior to initiating study treatment
   6. Plasmapheresis within 4 weeks prior to the initiation of study treatment
   7. Tasquinimod at any time
4. Known central nervous system involvement by myeloma
5. Diagnosis of smoldering multiple myeloma
6. Diagnosis of POEMS syndrome (plasma cell dyscrasia with polyneuropathy, organomegaly, endocrinopathy, monoclonal protein, and skin changes)
7. Active plasma cell leukemia
8. Symptomatic primary (AL) amyloidosis
9. Diagnosis of myelodysplastic syndrome or myeloproliferative syndrome
10. Active other malignancy
11. Major surgery within 4 weeks prior to initiating study treatment
12. Evidence of severe or currently uncontrolled cardiovascular condition
13. Ongoing or active systemic infection that requires systemic antibiotic or parenteral anti-infective therapy
14. Active tuberculosis, active hepatitis A, B or C virus infection, or known human immunodeficiency virus (HIV) positive
15. History of pancreatitis
16. History of malabsorption or other condition that would interfere with absorption of study drugs
17. Systemic treatment within 14 days prior to the initiation of study treatment with moderate or strong inhibitor or moderate or strong inducer of cytochrome P-3A4 (CYP3A4)
18. Need for ongoing therapy drug substances of narrow therapeutic range that are metabolized mainly by CYP3A4 (alfentanil, fentanyl, quinidine, astemizole, terfenadine, sirolimus, tacrolimus, cyclosporine, cisapride, ergotamine)
19. Need for ongoing therapy with drug substances of narrow therapeutic range metabolized mainly by CYP1A2 (duloxetine, alosetron, theophylline, tizanidine, ondansetron)
20. Ongoing treatment with warfarin, unless the INR is <=3.0.
21. For subjects enrolled on the IRd combination arms, prior dose-limiting toxicity with lenalidomide or ixazomib or absolute contraindication to concomitant thrombosis prophylaxis
22. Peripheral neuropathy grade ≥2 (NCI-CTCAE)
23. Known hypersensitivity to tasquinimod or any excipients in the study treatments
24. Pregnant or nursing (lactating) women
25. Any other condition that would, in the Investigator's judgment, contraindicate subject's participation in the clinical study due to safety concerns or compliance with clinical study procedures
26. Prior inclusion in this study