Open Label Phase 1/2 Study of Tasquinimod in Patients With Primary Myelofibrosis (PMF), Post-Polycythemia Vera Myelofibrosis (Post-PV MF), or Post-Essential Thrombocytosis Myelofibrosis (Post-ET MF)

Inclusion Criteria: 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. Exclusion Criteria: Participants eligible for this study must not meet any of the following criteria: * Any concurrent severe and/or uncontrolled medical conditions that could increase the participant's risk for toxicity while in the study or that could confound discrimination between disease- and study treatment-related toxicities. * Impaired cardiac function or clinically significant cardiac diseases, including any of the following: * History or presence of ventricular tachyarrhythmia. * Presence of unstable atrial fibrillation (ventricular response \> 100 bpm); Participants with stable atrial fibrillation are eligible, provided they do not meet any of the other cardiac exclusion criteria. * Clinically significant resting bradycardia (\< 50 bpm). * Angina pectoris or acute myocardial infarction ≤ 3 months prior to starting study drug. * Other clinically significant heart disease (e.g., symptomatic congestive heart failure; uncontrolled arrhythmia or hypertension; history of labile hypertension or poor compliance with an antihypertensive regimen). * Participants who are currently receiving chronic (\> 14 days) treatment with corticosteroids at a dose ≥ 10 mg of prednisone (or its glucocorticoid equivalent) per day, or any other chronic immunosuppressive treatment that cannot be discontinued prior to starting study drug. * Treatment with chemotherapy (except hydroxyurea within 1 day prior to study treatment), immunomodulatory drug therapy (e.g. thalidomide, interferon-alpha), platelet-reducing therapy (e.g. anagrelide), immunosuppressive therapy, and erythropoetin use within 28 days prior to study treatment * Treatment with experimental therapy within the past 2 weeks or 5 half-lives, whichever is shorter * Treatment with tasquinimod at any time * Participants with impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of tasquinimod as per physician opinion * Participants with known or active (acute and chronic) Hepatitis A, B, or C; and Hepatitis B and C carriers, HIV. Participants are excluded regardless of detectability of viral load (lack of safety data). * Participants with clinically significant bacterial, fungal, parasitic or viral infection which require therapy * History of pancreatitis * History of malabsorption or other condition that would interfere with absorption of study drugs (e.g. ulcerative diseases, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, small bowel resection) * Systemic treatment within 14 days prior to the initiation of study treatment with any of the following moderate or strong inhibitor, or moderate or strong inducer of cytochrome P-3A4 (CYP3A4): imidazoles (e.g. ketoconazole), protease inhibitors (e.g. ritonavir), macrolides (e.g. erythromycin), rifampicin, rifabutin, phenytoin, carbamazepine, St. John's wort. * Need for ongoing therapy with any of the following drug substances of narrow therapeutic range that are metabolized mainly by CYP3A4: alfentanil, fentanyl, quinidine, astemizole, terfenadine, sirolimus, tacrolimus, cyclosporine, cisapride, and ergotamine * Need for ongoing therapy with any of the following drug substances of narrow therapeutic range metabolized mainly by CYP1A2: duloxetine, palonosetron, theophylline, tizanidine, and ondansetron. * Need for ongoing therapy with any of the following drug substances of narrow therapeutic range metabolized mainly by CYP2D6: Dosulepin, Flecainide, Sotalol, Pimozide, Procainamide, Clonidine, Desipramine, Clomipramine, Amitriptyline, Imipramine, Nortriptyline, Trimipramine, Amoxapine, Dronedarone, Phenytoin * Ongoing treatment with warfarin, unless the INR is \<=3.0. * Known hypersensitivity to tasquinimod or any excipients in the study treatments * 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 * Prior inclusion in this study * Pregnant women are excluded from this study because tasquinimod is an agent with the potential for teratogenic or abortifacient effects. Because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with tasquinimod, breastfeeding should be discontinued if the mother is treated with tasquinimod. These potential risks may also apply to other agents used in this study.