Study to Evaluate Safety, Pharmacokinetic and Pharmacodynamic Dose Escalation and Expansion Study of PXS-5505 in Patients With Primary, Post-polycythemia Vera or Post-essential Thrombocythemia Myelofibrosis

Inclusion Criteria: * Have a pathologically confirmed established diagnosis of primary myelofibrosis or post-essential thrombocythemia/polycythemia vera myelofibrosis as per the World Health Organization 2016 diagnostic criteria (must include at least Grade 2 marrow fibrosis) * Patients who are not eligible for stem cell transplantation * a) Dose escalation / Cohort expansion phase only: Patients not currently on ruxolitinib or fedratinib (where available) treatment due to ineligibility, or previously treated patients who have been discontinued for at least 2 weeks prior to first dose of study drug due to any of the following criteria: * Ineligible: Platelets \<50 x 10\^9/L * Intolerant: Development of red blood cell transfusion dependence of at least two units/month for 2 months OR ≥Grade 3 adverse events of thrombocytopenia, anemia, hematoma, and/or hemorrhage while on treatment with ruxolitinib or fedratinib for at least 28 days * Refractory: \< 10% spleen volume reduction by MRI or CT, or \< 30% decrease from baseline in spleen volume by palpation after at least 3 months treatment with ruxolitinib or fedratinib * Relapsed: Regrowth to \< 10% spleen volume reduction by MRI or CT, or \< 30% decrease from baseline in spleen volume by palpation, following an initial response to ruxolitinib or fedratinib and after at least 3 months treatment * b) Add-on phase only: Are being treated with ruxolitinib for at least 12 weeks prior to first administration of study treatment. The patient must be on a stable dose (no dose adjustments) of ruxolitinib for ≥ 8 weeks prior to study treatment and have not achieved complete remission (CR) by International Working Group (IWG) criteria. * Have intermediate -2, or high-risk disease according to the International Working Group prognostic scoring system (DIPSS); * a) Dose escalation / Cohort expansion phase only: Have symptomatic disease according to the MFSAF v4.0; Symptomatic disease is defined as a score of at least one in at least two items of the MFSAF v4.0; b) Add-on phase only: have a score of ≥ 10 on the MFSAF v4.0; * Have symptomatic disease according to the MFSAF v4.0; * Life expectancy of six months or greater; * Must have adequate organ function as demonstrated by the following (within last 2 weeks): * Alanine aminotransferase and/or aspartate aminotransferase ≤ 2.5x upper limit of normal (ULN), or ≤ 4 x ULN (if upon judgment of the treating physician, it is believed to be due to extramedullary hematopoiesis \[EMH\] related to MF); * Direct bilirubin ≤ 1.5 x ULN; or ≤ 2 x ULN (if upon judgment of the treating physician, it is believed to be due to EMH related to MF); * Estimated glomerular filtration rate (eGFR) \> 50 mL/min * Eastern Cooperative Oncology Group performance status ≤ 2; * Men must agree to using one medically approved contraceptive measure and have their partners agree to an additional barrier method of contraception for the duration of the study and for 90 days after the last administration of study drug; women of childbearing potential must use effective contraception * Cohort Expansion and Add-on Phase only: A bone marrow biopsy must have been performed within 3 months prior to Day 1 treatment to establish the baseline fibrosis score or within 6 months of the re-initiation of treatment with PXS-5505 if subject participated in dose escalation phase of the trial Exclusion Criteria: * Greater than (\>) 10% blasts in peripheral blood (determined within last two weeks); * Prior splenectomy, or planning to undergo splenectomy, or splenic irradiation within 3 months prior to the first dose of study treatment * Any serious medical condition or psychiatric illness that would prevent (as judged by the treating physician) the subject from signing the informed consent form or any condition, including the presence of laboratory abnormalities, which places the subject at unacceptable risk if he/she were to participate in the study or confounds the ability to interpret data from the study * Known history of human immunodeficiency virus, active hepatitis C, or active hepatitis B * History or presence of any form of cancer within the three years prior to enrolment, with the exception of excised basal cell or squamous cell carcinoma of the skin, or cervical carcinoma in situ or breast carcinoma in situ that has been excised or resected completely and is without evidence of local recurrence or metastasis * Participation in an investigational drug or device trial within two weeks prior to study Day 1 or within five times the half-life of the investigational agent in the other clinical study, if known * Use of any cytotoxic chemotherapeutic agents, including hydroxyurea, corticosteroids (prednisone ≤ 10 mg/day or corticosteroid equivalent is allowed), or immune modulators (e.g., thalidomide) within two weeks and interferon use within four weeks prior to study Day 1 * Symptomatic congestive heart failure (New York Heart Association Classification Class II), unstable angina, or unstable cardiac arrhythmia requiring medication * Pregnancy * History of surgery within two weeks prior to enrolment or anticipated surgery during the study period or two weeks post-study * History of aneurysm * Any other condition that might reduce the chance of obtaining data required by the protocol or that might compromise the ability to give truly informed consent.