. Current use or prior use of immunosuppressive medication within weeks prior to first dose of TAB, with the exception of intranasal and inhaled corticosteroids or systemic corticosteroids not to exceed mg/day of prednisone or equivalent; Current or prior use of immunosuppressive medication within days before the first dose of study therapy with the exceptions of intranasal corticosteroids or systemic corticosteroids at physiological doses that do not exceed mg/day of prednisone or an equivalent corticosteroid. Diagnosis of immunodeficiency or is receiving systemic steroid therapy or any other form of immunosuppressive therapy within days prior to the first dose of study treatment, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days before the first dose of durvalumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Are currently receiving or have had prior use of immunosuppressive medication within days before the first dose of study drug, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed milligrams/day of prednisone, or an equivalent corticosteroid. Current or prior use of immunosuppressive medication within days before the first dose of treatment on this protocol, with the exceptions of:\r\n* Intranasal and inhaled corticosteroids\r\n* Systemic corticosteroids at physiologic doses not to exceed mg/day of prednisone or equivalent\r\n* Premedication for hypersensitivity reactions (e.g. to computed tomography [CT] contrast for scans). Use of intranasal and inhaled corticosteroids or systemic corticosteroids at physiologic doses not to exceed mg/day of prednisone or equivalent is permitted. Current or prior use of immunosuppressive medication within days before the first dose of durvalumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days before the first dose of durvalumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days before the first dose of durvalumab or tremelimumab, with the exceptions of: intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid or steroids as pre-medication for hypersensitivity reactions (e.g. CT scan premedication). Current use or prior use of immunosuppressive medication within days before the first dose of durvalumab, with the exceptions of intranasal, inhaled, and intra-articular corticosteroids or systemic corticosteroids at physiological doses which are not to exceed mg/day of prednisone or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days before the first dose of durvalumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days before the first dose of durvalumab or tremelimumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days before the first dose of durvalumab or tremelimumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days before the first dose of durvalumab or tremelimumab with the exceptions of premedication and intranasal, topical and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days before the first dose of durvalumab or tremelimumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days before the first dose of durvalumab or tremelimumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days before the first dose of durvalumab OR tremelimumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid. Steroid premedication for the prevention of radiologic contrast hypersensitivity is allowed. Current or prior use of immunosuppressive medication within days before the first dose of durvalumab (MEDI) or tremelimumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days before the first dose of durvalumab or tremelimumab, with the exceptions of intranasal, topical, and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days before the first dose of durvalumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days before the first dose of durvalumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days before the first dose of nivolumab, with the exceptions of intranasal, topical, and inhaled corticosteroids or systemic corticosteroids at physiologic doses not to exceed mg/day of prednisone or equivalent (use for brain metastases is not permitted days prior to start of therapy) Current or prior use of immunosuppressive medication within days before the first dose of durvalumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days before the first dose of durvalumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days before the first dose of durvalumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days before the first dose of durvalumab or tremelimumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days before the first dose of MEDI and tremelimumab with the exceptions of intranasal and inhaled corticosteroids, systemic corticosteroids at physiologic doses not to exceed mg/day of prednisone or equivalent, or steroids used transiently to control contrast agent allergies for radiographic studies Current or prior use of immunosuppressive medication within days before the first dose of MEDI, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive therapy within days before the first dose of durvalumab or tremelimumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid PHASE I STUDY ELIGIBILITY CRITERIA:\r\nCurrent or prior use of immunosuppressive medication within days before the first dose of MEDI, with the exception of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone or an equivalent corticosteroid; in the case of short term use of systemic corticosteroids (less than hours within days) of greater than mg/day of prednisone or an equivalent corticosteroid, the required washout period prior to starting the first dose of MEDI is days PHASE II STUDY COHORT OVARIAN CANCER ELIGIBILITY CRITERIA (MEDI+O, MEDI+C AND MEDI+O+C):\r\nCurrent or prior use of immunosuppressive medication within days before the first dose of MEDI, with the exception of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone or an equivalent corticosteroid; in the case of short term use of systemic corticosteroids (less than hours within days) of greater than mg/day of prednisone or an equivalent corticosteroid, the required washout period prior to starting the first dose of MEDI is days PHASE II STUDY COHORT TRIPLE NEGATIVE BREAST CANCER ELIGIBILITY CRITERIA (MEDI+O ONLY):\r\nCurrent or prior use of immunosuppressive medication within days before the first dose of MEDI, with the exception of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone or an equivalent corticosteroid; in the case of short term use of systemic corticosteroids (less than hours within days) of greater than mg/day of prednisone or an equivalent corticosteroid, the required washout period prior to starting the first dose of MEDI is days PHASE II STUDY METASTATIC CASTRATE-RESISTANT PROSTATE CANCER COHORT ELIGIBILITY CRITERIA (MEDI+O ONLY):\r\nCurrent or prior use of immunosuppressive medication within days before the first dose of MEDI, with the exception of intranasal, inhaled, ophthalmological, or topical corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone or an equivalent corticosteroid; in the case of short term use of systemic corticosteroids (less than hours within days) of greater than mg/day of prednisone or an equivalent corticosteroid, the required washout period prior to starting the first dose of MEDI is days PHASE II COLORECTAL CANCER COHORT (MEDI+C ONLY):\r\nCurrent or prior use of immunosuppressive medication within days before the first dose of MEDI, with the exception of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone or an equivalent corticosteroid; in the case of short term use of systemic corticosteroids (less than hours within days) of greater than mg/day of prednisone or an equivalent corticosteroid, the required washout period prior to starting the first dose of MEDI is days Current or prior use of immunosuppressive medication within days before the first dose of MEDI, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Active or prior history of autoimmune or inflammatory condition requiring ongoing immunosuppressive medications. This specifically includes use of immunosuppressive medication within days before the first dose of durvalumab with the exceptions of intranasal corticosteroids or systemic corticosteroids at physiological doses, which do not exceed mg/day of prednisone or an equivalent corticosteroid. Current or prior use of immunosuppressive medication within days before the first dose of durvalumab and tremelimumab with the exceptions of intranasal and inhaled corticosteroids, systemic corticosteroids at physiologic doses not to exceed mg/day of prednisone or equivalent, or steroids used transiently to control contrast agent allergies for radiographic studies Current or prior use of immunosuppressive medication within days prior to first study dose, with the exception of intranasal and inhaled corticosteroids or systemic corticosteroids at physiologic doses not to exceed mg/day of prednisone or equivalent. Steroids as premedication for hypersensitivity reactions due to radiographic contrast agents are allowed. Current or prior use of immunosuppressive medication within days before the first dose of durvalumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid; live attenuated vaccines within days of durvalumab dosing (ie, days prior to the first dose, during treatment with durvalumab and for days post discontinuation of durvalumab); inactivated vaccines, such as the injectable influenza vaccine, are permitted Current or prior use of immunosuppressive medication within days before the first dose of PD , with the exceptions of intranasal and inhaled corticosteroids and systemic corticosteroids at physiological doses (defined as not exceeding mg/day of prednisone, or an equivalent dose of over corticosteroid) Current or prior use of immunosuppressive medication within days before step registration, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days before the first dose of MEDI, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days before the first dose of durvalumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days before the first dose of treatment, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Patients must not have received any immunosuppressive medication within days prior to sub-study registration and must not be planning to receive any such agents while on protocol treatment; however, intranasal and inhaled corticosteroids or systemic corticosteroids at physiologic doses not to exceed mg/day of prednisone or equivalent are allowed Patients must not have received any immunosuppressive medication within days prior to RE-TREATMENT registration and must not be planning to receive any such agents while on protocol treatment; however, intranasal and inhaled corticosteroids or systemic corticosteroids at physiologic doses not to exceed mg/day of prednisone or equivalent are allowed Current or prior use of immunosuppressive medication within days before the first dose of MEDI with the exceptions of intranasal and inhaled corticosteroids, or systemic corticosteroids in Cohort C Current or prior use of immunosuppressive medication within days before the first dose of durvalumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid; steroid pre-medication for CT scan contrast or study drug, is allowable, regardless of dose Current or prior use of immunosuppressive medication within days before the first dose of durvalumab (MEDI) or tremelimumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone or any corticosteroid for less than consecutive days Current or prior use of immunosuppressive medication within days before the first dose of durvalumab or durvalumab and tremelimumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid; patients who have received acute, low dose, systemic immunosuppressant medications (e.g., dexamethasone for nausea or steroids as CT scan contrast premedication) may be enrolled Current or prior use of immunosuppressive medication within days before the first dose of durvalumab, with the exceptions of intranasal and inhaled corticosteroids or systemic (oral or iv) corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days before the first dose of durvalumab or tremelimumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days before the first dose of durvalumab, with the exceptions of intranasal and inhaled corticosteroids or systemic corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid (steroids as pre-med for hypersensitivity reactions eg. computed tomography (CT) scan premedication is acceptable) Current or prior use of immunosuppressive medication within days of treatment on protocol, with the exception of intranasal and inhaled corticosteroids or oral corticosteroids at physiological doses, which are not to exceed mg/day of prednisone, or an equivalent corticosteroid Current or prior use of immunosuppressive medication within days prior to first study dose, with the exception of intranasal and inhaled corticosteroids or systemic corticosteroids at doses not to exceed mg/day of prednisone or equivalent. Steroids as premedication for hypersensitivity reactions due to radiographic contrast agents are allowed.