History of allergic reactions attributed to compounds of similar chemical or biologic composition to AZD or cisplatin Has a history of allergic reactions attributed to the study treatments (AZD or durvalumab), assigned chemotherapy agents, their compounds, or agents of similar chemical or biologic composition (e.g., antibody therapeutics) History of allergic reactions attributed to compounds of similar chemical or biologic composition to AZD History of clinically significant allergic reactions attributed to compounds of similar chemical or biologic composition to AZD or docetaxel or to docetaxel itself Has a history of allergic reactions attributed to the study treatments (AZD or MEDI), their compounds, or agents of similar chemical or biologic composition (eg, antibody therapeutics) History of allergic reactions attributed to compounds of similar chemical or biologic composition to AZD (osimertinib) or bevacizumab History of allergic reactions to study compounds or excepients Additional exclusion criteria Part A: Patients with clinically active brain metastases and prior exposure to AZD, AZD, MEDI, or any other anti PD (L) antibody. History of allergic reactions attributed to compounds of similar chemical or biologic composition to AZD or other agents used in study Patients must NOT have history of allergic reactions attributed to compounds of similar chemical or biologic composition to nab-paclitaxel, gemcitabine or AZD PHASE II: Patients must NOT have history of allergic reactions attributed to compounds of similar chemical or biologic composition to nab-paclitaxel, gemcitabine or AZD History of allergic reactions attributed to compounds of similar chemical or biologic composition to AZD or cyclosporine A or their excipients History of allergic reactions attributed to compounds of similar chemical or biologic composition to AZD or cisplatin History of allergic reactions attributed to compounds of similar chemical or biologic composition to AZD (MK-) or gemcitabine History of allergic reactions attributed to compounds of similar chemical or biologic composition to AZD History of allergic reactions attributed to compounds of similar chemical or biologic composition to AZD or belinostat SELUMETINIB ARM: History of allergic reactions attributed to compounds of similar chemical or biologic composition to AZD (selumetinib) Patients with a history of allergic reactions attributed to compounds of similar chemical or biologic composition to temozolomide or AZD (MK-) are ineligible; the AZD (MK-) investigator brochure and the temozolomide package insert can be referenced for more information History of hypersensitivity attributed to compounds of similar chemical or biologic composition to MLN (TAK-) or osimertinib (AZD)