Trial of Selumetinib and Bromodomain Inhibitor With Durvalumab for Sarcomas

Inclusion Criteria: Inclusion Criteria AGE: ≥ 18 years of age Weight: \>30 kg Life expectancy of at least 12 weeks Part A and B (Phase 1): Patients with histologically confirmed soft tissue or bone sarcoma of the following subtypes: * MFH/ undifferentiated pleomorphic sarcoma * Unclassified sarcoma * Rhabdomyosarcoma * Malignant peripheral nerve sheath tumor (MPNST) * Osteosarcoma * Ewing or Ewing-like sarcoma * Synovial sarcoma * Desmoplastic small round blue cell tumor (DSRCT) Patients must have progressed or demonstrated disease that is refractory to standard therapies. Patients for whom no standard of care treatments exist are eligible. Part C (Phase 2): Patients with progressive, relapsed, unresectable or metastatic NF associated MPNST. MEASURABLE DISEASE: Patients must have evaluable or measurable disease (Phase 1) and measurable disease by RECISTv1.1 (Phase 2). * Patients must have fully recovered from the acute toxic effects of all prior chemotherapy, immunotherapy, or radiotherapy prior to entering on this study excluding chronic grade 1 toxicities and alopecia. * No limitation on the number of prior chemotherapy regimens that the patient may have received prior to study entry. * Myelosuppressive chemotherapy: The last dose of all myelosuppressive anticancer drugs must be at least 3 weeks (≥21 days) and 42 days if prior nitrosourea prior to study entry. * Immunotherapy: The last dose of immunotherapy (monoclonal antibody or vaccine) must be at least 4 weeks prior to study entry. * Biologic (anti-cancer agent): The last dose of all biologic agents for the treatment of the patient's cancer (such as retinoids or tyrosine kinase inhibitors) must be at least 7 days prior to study entry. Prior therapy with a MEK, Ras, or Raf inhibitor used for treatment of malignant sarcoma is not allowed. Prior therapy of MEK, Ras, or Raf inhibitor for other tumor such as plexiform neurofibroma or glioma is allowed. * Radiation therapy: The last dose of radiation to more than 25% of marrow containing bones (pelvis, spine, skull) must be at least 4 weeks prior to study * Radiation therapy: The last dose of radiation to more than 25% of marrow containing bones (pelvis, spine, skull) must be at least 4 weeks prior to study entry. The last dose of all other local palliative (limited port) radiation must be at least 2 weeks prior to study entry. * Stem Cell Transplantation. At least 2 months post-autologous stem cell transplant. * Growth Factors. The last dose of colony stimulating factors, such as filgrastim, sargramostim, and erythropoietin, must be at least 1 week prior to study entry, the last dose of long-acting colony stimulating factors, such as pegfilgrastim, must be at least 2 weeks prior to study entry. * Karnofsky performance level ≥ 50% (See Appendix II). * Patients who are unable to walk because of paralysis or motor weakness, but who are able to use a wheelchair will be considered ambulatory for the purpose of calculating the performance score. Hemoglobin ≥9.0 g/dL (transfusion permissible) * Peripheral absolute neutrophil count (ANC) of ≥1000/µL * Platelet count ≥100,000/µL (transfusion independent (no transfusion within at least 7 days prior to enrollment)) * Total bilirubin must be ≤ 1.5 times the upper limit of normal (ULN) * SGOT (AST)/SGPT (ALT) must be ≤ 3.0 times ULN unless liver metastases are present, in which case it must be ≤ 5x ULN RENAL FUNCTION: Serum creatinine ≤ 1.5 times ULN or measured reatinine clearance \>50 mL/min or calculated creatinine clearance \> 50 mL/min by the Cockcroft- Gault formula (Cockgraft and Gault 1976) or by the 24 hour urine collection for determination of creatinine clearance * Normal ejection fraction (ECHO or cardiac MRI) ≥53% (or the institutional normal; if a range is given then the upper value of the range will be used) * QTC or QTcF ≤ 450msec Fertile men and women of childbearing potential must agree to use an effective method of birth control. Female participants of childbearing potential must be willing to practice highly effective contraception as detailed below from the time of screening until 3 months after discontinuing the study. They must not be breastfeeding and must have negative pregnancy test prior to start of dosing. For a female participant to be considered as of not childbearing potential, she should fulfil one of the following: Post-menopausal women, defined as either women aged more than 50 years and have amenorrhea for at least 12 months following cessation of all exogenous hormonal treatments, or, women under 50 years who have amenorrhea for at least 12 months following cessation of exogenous hormonal treatments, and have serum follicle-stimulating hormone (FSH) and luteinizing hormone (LH) levels in the postmenopausal range for the institution. or * Have documentation of irreversible surgical sterilization by hysterectomy, bilateral oophorectomy or bilateral salpingectomy (but not tubal ligation) * Have medically confirmed, irreversible premature ovarian failure. Highly effective methods of contraception are: * Use of medroxyprogesterone acetate depot injection (Depo-proveraTM). (Please note: use of any other oral, injected, or implanted hormonal methods of contraception cannot be considered highly effective as it is currently unknown whether investigational agents may reduce their effectiveness) * Placement of a copper-banded intrauterine device (IUD) or intrauterine system (IUS) * Bilateral tubal ligation * Vasectomized partner Barrier methods include: Occlusive cap (e.g. diaphragm or cervical/vault caps) with spermicide Male participants should either be surgically sterile or willing to use an effective barrier method of contraception during the study and for 3 months following the last dose of drug therapy if sexually active with a female of childbearing potential. If not done, storage of sperm prior to receiving drug therapy will be advised to male participants with a desire to have children. M