Ivosidenib and Ruxolitinib in Patients With Advanced Myeloproliferative Neoplasms (MPNs) That Have an IDH1 Gene Mutation

Inclusion Criteria: * Advanced-Phase IDH1-mutated Ph-negative MPNs (both untreated and relapsed/refractory) including any of the following: * polycythemia vera with (PV) ≥ 5% peripheral or bone marrow blasts at time of screening * essential thrombocythemia (ET) with ≥ 5% peripheral or bone marrow blasts at time of screening * primary myelofibrosis (PMF) with ≥ 5% peripheral or bone marrow blasts at time of screening * Atypical CML with ≥ 5% peripheral or bone marrow blasts at time of screening * MPN-NOS with ≥ 5% peripheral or bone marrow blasts at time of screening * MDS/MPN Overlap Syndromes including CMML with ≥ 5% peripheral or bone marrow blasts at time of screening * post-PV myelofibrosis with ≥ 5% blasts peripheral or bone marrow blasts at time of screening * post-ET myelofibrosis with ≥ 5% blasts peripheral or bone marrow blasts at time of screening * primary and secondary myelofibrosis with inadequate response to JAK inhibitor regardless of blast percentage. Inadequate response to JAK inhibitor will be defined as lack of achieving any clinical improvement criteria within 12 weeks of of JAK inhibitor initiation. * Patients can be on cytoreduction at time of study enrollment with hydroxyurea or steroids. * Age ≥18 years. * ECOG performance status ≤2 * Patients must have normal organ and marrow function as defined below: * Creatinine clearance ≥60 mL/min, determined by the Cockroft-Gault formula, OR serum creatinine ≤ 1.5 x ULN * AST and ALT ≤3 x ULN and bilirubin ≤1.5 x ULN (unless considered due to Gilbert's syndrome, leukemic involvement, or extravascular hemolysis in the spleen) * A platelet count of 50 x 109/L should be met for those with chronic-phase myelofibrosis and \< 5% blasts peripherally or in bone marrow * HIV-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months are eligible for this trial. * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated. Patients with a history of hepatitis C virus (HCV) infection must have been treated and cured. For patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load. * Other eligibility criteria include the following: * Patients must be at least 4 weeks from major surgery, radiation therapy, or participation in other investigational trials, and must have recovered from clinically significant toxicities related to these prior treatments. * The effects of the investigational agents 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. * Ability to understand and the willingness to sign a written informed consent document. Exclusion Criteria: * Patients cannot be on concomitant chemotherapy, radiation therapy, or immunotherapy other than as specified in this protocol. Patients cannot have had prior treatment with ivosidenib. * Patients with a "currently active" second malignancy other than non-melanoma skin cancers. Patients are not considered to have a "currently active" malignancy if they have completed therapy and are free of disease or they are not currently requiring treatment for an indolent malignancy. Patients with APL and active CNS disease would also be excluded * History of allergic reactions attributed to compounds of similar chemical or biologic composition to ivosidenib or ruxolitinib. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, venous thromboembolism, stroke, active chronic liver disease (eg chronic alcoholic liver disease, autoimmune hepatitis, sclerosing cholangitis, primary biliary cholangitis, hemochromatosis) or psychiatric illness/social situations that would limit compliance with study requirements. * Subject has QTc interval ≥ 450 msec or other factors that increase the risk of QT prolongation or arrhythmic events at screening unless due to bundle branch block or pacemaker with approval of the principal investigator. * Pregnant women are excluded from this study because ruxolitinib and ivosidenib carry 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 ruxolitinib and ivosidenib, breastfeeding should be discontinued if the mother is treated with any of these agents. * Patient is known to have dysphagia, short-gut syndrome, gastroparesis, or other conditions that limit the ingestion or gastrointestinal absorption of drugs administered orally. * Patients receiving any medications or substances that are inhibitors or inducers of CYP3A4 should have eligibility and alternative medications reviewed by site PI.