A multi-arm multi-stage (MAMS) phase 1/2 study. Phase 1 will be conducted in BCG-unresponsive NMIBC patients to establish the safety of durvalumab monotherapy (cohort 1) and durvalumab in combination with BCG (cohort 2a) and external beam radiation therapy (EBRT) (cohort 2b). Provided safety is demonstrated and recommended phase 2 doses (RP2D) are established in phase 1, the study will proceed to phase 2 testing. Phase 2 will be conducted in the BCG-relapsing NMIBC population. In phase 2, BCG-relapsing NMIBC subjects will be randomized between treatment arms examining intravesical BCG in combination with novel immunotherapy agents (durvalumab), novel immunotherapy in combination with radiation (durvalumab + EBRT), or retreatment with intravesical BCG. In addition to providing additional safety data on the combination regimens studied, phase 2 will provide preliminary efficacy profiles for BCG-relapsing NMIBC subjects with and without CIS treated with each regimen. For regimens demonstrating a tolerable safety profile and encouraging clinical activity in this phase 1/2 design, a randomized phase 3 trial of experimental arm therapy versus re-treatment with intravesical BCG therapy would be considered.