Multi-Arm Study to Test the Efficacy of Immunotherapeutic Agents in Multiple Sarcoma Subtypes

Inclusion Criteria: 1. Age: \>/= 18 years of age 2. Histologically or cytologically confirmed sarcoma that fall into one of the following categories Patients with low-grade tumors are eligible if there is definite evidence of metastasis or progression (defined as at least a 10% increase in the cumulative sum of the longest diameters within a 3 month period): 1. Adipocytic tumors (Well-differentiated/dedifferentiated liposarcoma, myxoid liposarcoma, pleomorphic liposarcoma) 2. Vascular tumors (leiomyosarcoma, angiosarcoma) 3. Undifferentiated pleomorphic sarcoma 4. Synovial sarcoma 5. Osteosarcoma 6. Other sarcoma histologies 3. Must have received and have progressed, are refractory or intolerant to standard therapy appropriate for the specific sarcoma subtype, if there is a standard therapy for the subtype (i.e. Progressing well-differentiated liposarcoma, clear cell sarcoma etc do not require prior therapy). 4. Subjects must have at least 1 lesion that is measurable by irRECIST a. A previously irradiated lesion can be considered a target lesion if the lesion is well defined, measurable per irRECIST, and has clearly progressed. b. Subjects undergoing fresh tumor biopsies must have additional non-target lesions that can be biopsied at acceptable risk as judged by the investigator or if no other lesion suitable for biopsy, then an irRECIST target lesion used for biopsy must be \>/= 2 cm in longest diameter. 5. Subjects must consent to provide archived tumor specimens for correlative biomarker studies. Tumor tissue must be identified and availability confirmed prior to initiation of study therapy. In the setting where archival material is unavailable or unsuitable for use, or there have been multiple intervening therapies subjects must consent and undergo fresh tumor biopsy. A tumor lesion planned for biopsy must not be an irRECIST target lesion unless there are no other lesions suitable for biopsy and lesion used for biopsy is \>/= 2 cm in longest diameter. 6. ECOG performance status of 0 or 1 7. Adequate organ function as determined by (lymphocyte count): a. Hematological (without growth factor or transfusion support): i. Absolute neutrophil count \>/= 1.5 x 10\^9/L (1,500/mm\^3) ii. Platelet count \>/= 90 × 10\^9/L (100,000/mm\^3) iii. Hemoglobin \>/= 8.0 g/dL within first 2 weeks prior to first dose of investigational product b. Renal: i. Calculated creatinine clearance (CrCl) or 24-hour urine CrCl \> 50 mL/min Cockcroft-Gault formula (using actual body weight) will be used to calculate CrCl, except for pts with Osteosarcoma who will be allowed to participate with an estimated creatinine clearance (CrCl) of \> 40 mL/min, as calculated by the Cockcroft-Gault equation. c. Hepatic: i. Total bilirubin \</= 1.5 × ULN; for subjects with documented/suspected Gilbert's disease, bilirubin \</= 3 × ULN ii. AST and ALT \</= 2.5 × ULN; for subjects hepatic metastases, ALT and AST \</= 5 × ULN 8. Females of childbearing potential who are sexually active with a nonsterilized male partner must use a highly effective method of contraception from the time of screening, and must agree to continue using such precautions for 180 days after the final dose of investigational product. 9. Life expectancy of at least 6 months. 10. Ability to understand the purposes and risks of the study and has signed a written consent form approved by the investigator's IRB/Ethics Committee Exclusion Criteria: 1. Prior therapy with anti-PD1, anti-PD-L1 or anti-CTLA-4 antibody 2. Active or prior documented autoimmune disease (including inflammatory bowel disease, celiac disease, Wegener syndrome) within the past 2 years. Subjects with childhood atopy or asthma, vitiligo, alopecia, Hashimoto syndrome, Grave's disease, or psoriasis not requiring systemic treatment (within the past 2 years) are not excluded. 3. Untreated central nervous system metastatic disease, leptomeningeal disease, or cord compression. Subjects previously treated central nervous system metastases that are radiographically and neurologically stable for at least 6 weeks and do not require corticosteroids (of any dose) for symptomatic management for at least 14 days prior to first dose of MEDI4736 and tremelimumab are permitted to enroll. 4. Concurrent enrollment in another clinical study, unless it is an observational (non-interventional) clinical study or the follow-up period of an interventional study. 5. Receipt of any conventional or investigational anticancer therapy not otherwise specified above within 28 days or 5 half-lives of the agent prior to the first dose of durvalumab and tremelimumab. 6. Any concurrent chemotherapy, Immunotherapies or biologic or hormonal therapy for cancer treatment. Concurrent use of hormones for non-cancer-related conditions (eg, insulin for diabetes and hormone replacement therapy) is acceptable. In addition, local treatment (eg, by local surgery or radiotherapy) of isolated lesions for palliative intent is acceptable beyond the first cycle with prior consultation and in agreement with the PI. 7. Unresolved toxicities from prior anticancer therapy, defined as having not resolved to NCI CTCAE v4.03 Grade 0 or 1 with the exception of alopecia and laboratory values listed per the inclusion criteria. Subjects with irreversible toxicity that is not reasonably expected to be exacerbated by any of the investigational products may be included (eg, hearing loss) after consultation with the study chair. 8. Current or prior use of immunosuppressive medication within 14 days prior to the first dose of MEDI4736 or tremelimumab. The following are exceptions to this criterion: a. Intranasal, inhaled, topical steroids, or local steroid injections (eg, intra-articular injection), b. Systemic corticosteroids at physiologic doses not to exceed 10 mg/day of prednisone or equivalent, c. Steroids as premedication for hypersensitivity reactions (eg, computed tomography \[CT\] scan premedication). 9. History of primary immunodeficiency, solid organ transplantation, or previous clinical diagnosis of tuberculosis 10. True positive test results for human immunodeficiency virus (HIV) or hepatitis B or C. 11. Receipt of live, attenuated vaccine within 28 days prior to the first dose of investigational products (NOTE: Subjects, if enrolled, should not receive live vaccine during the study and 180 days after the last dose of investigational products). 12. Major surgery (as defined by the investigator) within 4 weeks or thoracotomy for pulmonary metastases within 2 weeks prior to first dose of treatment or if still recovering from prior surgery. Local surgery of isolated lesions for palliative intent is acceptable. 13. Other invasive malignancy within 2 years except for noninvasive malignancies such as cervical carcinoma in situ, non-melanomatous carcinoma of the skin or ductal carcinoma in situ of the breast that has/have been surgically cured. 14. Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, uncontrolled hypertension, unstable angina pectoris, cardiac arrhythmia, active peptic ulcer disease or gastritis, or psychiatric illness/social situations that would limit compliance with study requirement, substantially increase risk of incurring AEs from MEDI4736 or tremelimumab, or compromise the ability of the subject to give written informed consent. 15. Any condition that, in the opinion of the investigator or sponsor, would interfere with evaluation of the investigational product or interpretation of subject safety or study results. 16. Patients with a history of pneumonitis or interstitial lung disease.