∙ Participants eligible for inclusion in this study have to meet the following criteria:

∙ Myelofibrosis MF Monotherapy:

∙ Participants who are not candidates for, intolerant of, or relapsed/refractory to approved JAKi (ruxolitinib and / or fedratinib / pacritinib) or when further benefit from therapy is not anticipated per investigator. Participants not eligible for JAKi therapy irrespectively of previous treatments. Prior JAKi therapy is not required.

∙ Myelofibrosis Ruxolitinib Combination MF participants treated with Ruxolitinib for at least 3 months on a stable, uninterrupted dose for at least 2 months prior to study enrollment AND have suboptimal response (palpable spleen of ≥5 cm, or total symptoms score of ≥10) or progressive anemia/thrombocytopenia/neutropenia.

∙ AND all the below criteria in both cohorts:

• Must be diagnosed with treatment requiring PMF or post ET/PV MF diagnosed according to the 2016 World Health Organization with intermediate -1, intermediate -2 or high-risk disease according to the DIPSS prognostic scoring system, or if with low risk disease then with symptomatic splenomegaly that is ≥ 5 cm below left costal margin by physical exam.

• Peripheral or bone marrow blasts must be \< 10%

• Participants must provide written informed consent.

• Age 18 years or older. Because no dosing or adverse event data are currently available on the use of tasquinimod as monotherapy or in combination with ruxolitinib in patients \<18 years of age, children are excluded from this study.

• Willing and able to comply with scheduled visits, treatment plan and laboratory tests.

• Participant is able to swallow and retain oral medication.

• ECOG performance status 0-2.

• Required baseline laboratory status:

‣ Absolute neutrophil count (ANC) ≥ 1.0 x 109/L (1000/mm3)

⁃ Serum direct bilirubin ≤ 1.0 x ULN (upper limit of normal)

⁃ AST (SGOT) or ALT (SGPT) \[if both measured, then this applies to both measurements\] ≤ 2.5 x ULN, except for participants with MF involvement of the liver who must have levels ≤ 5 x ULN

⁃ Glomerular Filtration Rate (GFR) of ≥ 30 ml/min based on Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation using serum or plasma creatinine or cystatin-C.

• Treatment-related toxicities from prior therapies must have resolved to Grade ≤ 1.

• At least 2 weeks from prior investigational MF-directed treatment (till the start of study drug). This excludes concurrent ruxolitinib which is allowed in combination cohort. Hydroxyurea is allowed as standard cytoreductive therapy up until one day prior to initiation of therapy with tasquinimod. No other standard of care therapy for MF is allowed (as specified in the exclusion criteria)

• For women of childbearing potential, a documented negative serum or urine pregnancy test within 14 days prior to the administration of study drug.

• The effects of tasquinimod on the developing human fetus are unknown. For this reason, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. (Refer to Pregnancy Assessment Policy MD Anderson Institutional Policy # CLN1114). This includes all female participants, between the onset of menses (as early as 8 years of age) and 55 years unless the patient presents with an applicable exclusionary factor which may be one of the following:

‣ Postmenopausal (no menses in greater than or equal to 12 consecutive months).

⁃ History of hysterectomy or bilateral salpingo-oophorectomy.

⁃ Ovarian failure (Follicle Stimulating Hormone and Estradiol in menopausal range, who have received Whole Pelvic Radiation Therapy).

⁃ History of bilateral tubal ligation or another surgical sterilization procedure.

• Approved methods of birth control are as follows: Hormonal contraception (i.e. birth control pills, injection, implant, transdermal patch, vaginal ring), Intrauterine device (IUD), Tubal Ligation or hysterectomy, Subject/Partner post vasectomy, Implantable or injectable contraceptives, and condoms plus spermicide. Not engaging in sexual activity for the total duration of the trial and the drug washout period is an acceptable practice; however periodic abstinence, the rhythm method, and the withdrawal method are not acceptable methods of birth control. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately.

• Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 6 months after completion of tasquinimod administration.

• Ability to understand and the willingness to sign a written informed consent document.