This dose finding/extension study consists of three parts: Part A will identify the MTD of the AZD2014/palbociclib combination on a background of fulvestrant (referred to as the triplet) in postmenopausal women with locally advanced/metastatic estrogen receptor positive (ER+) breast cancer. Part B will further characterize safety, tolerability, PK, and preliminary efficacy in single-arm dose expansion groups. Part C will investigate the efficacy of the triplet combination in a double-blind, placebo-controlled, stratified, parallel group extension.