A Phase Ib/III, Open-label, Randomised Study of Capivasertib Plus CDK4/6 Inhibitors and Fulvestrant Versus CDK4/6 Inhibitors and Fulvestrant in Hormone Receptor-Positive and Human Epidermal Growth Factor Receptor 2-Negative Locally Advanced, Unresectable or Metastatic Breast Cancer (CAPItello-292)

Key inclusion criteria for both phases: 1. Adult females (pre-/peri-/ and post-menopausal), and adult males. 2. Histologically confirmed HR+/ HER2- breast cancer determined from the most recent tumour sample (primary or metastatic) per the American Society of Clinical Oncology and College of American Pathologists guideline. To fulfil the requirement of HR+ disease, a breast cancer must express ER with or without co-expression of progesterone receptor. 3. Eligible for fulvestrant therapy and at least one of the following: palbociclib, ribociclib, or abemaciclib, as per local investigator assessment. Previous tolerance to specific CDK4/6 inhibitors and dose levels required. 4. Adequate organ and bone marrow functions. 5. Consent to provide a mandatory FFPE tumour sample. Key inclusion criteria only for phase III: 1. Previous treatment with an ET (tamoxifen, AI, or oral SERD) as a single agent or in combination, with radiological evidence of breast cancer recurrence or progression while on, or within 12 months of, completing a (neo)adjuvant ET regimen. 2. Provision of mandatory blood samples at screening for central testing using an investigational ctDNA test to be stratified based on PIK3CA/AKT1/PTEN status. 3. Be eligible for fulvestrant and at least one out of palbociclib or ribociclib (depending on the available CDK4/6i options at time of enrolment), as per local investigator assessment. 4. Have measurable lesion(s) according to Response Evaluation Criteria in Solid Tumours version 1.1 (RECIST v1.1) or, in the absence of measurable disease, lytic or mixed bone lesions that can be assessed by computed tomography (CT) or magnetic resonance imaging (MRI). Key exclusion criteria for both phases: 1. History of another primary malignancy except for malignancy treated with curative intent with no known active disease ≥ 2 years before the first dose of study intervention and of low potential risk for recurrence. 2. Radiotherapy within 2 weeks prior to study treatment initiation. 3. Major surgery or significant traumatic injury within 4 weeks of the first dose of study treatment. 4. Persistent toxicities (CTCAE Grade \>1) caused by previous anticancer therapy, excluding alopecia. Participants with irreversible toxicity that is not reasonably expected to be exacerbated by study intervention may be included (eg, hearing loss or peripheral sensory neuropathy) after consultation with the AstraZeneca study physician. 5. Spinal cord compression, brain metastases or leptomeningeal metastases unless these lesions are definitively treated (eg. radiotherapy, surgery) and clinically stable off steroids for management of symptoms for at least 4 weeks prior to study treatment initiation. 6. Any of the following cardiac criteria at screening: (a). Mean resting corrected QT interval (QTcF): (i) Participants to be treated with palbociclib:: QTcF ≥ 470 ms obtained from the average of 3 consecutive (triplicate) ECGs (ii) Participants to be treated with ribociclib: QTcF ≥ 450 ms obtained from the average of 3 consecutive (triplicate) ECGs (iii) Participants to be treated with abemaciclib (Phase Ib only): QTcF ≥ 470 ms obtained from the average of 3 consecutive (triplicate) ECGs (b). Any clinically important abnormalities in cardiac rhythm, conduction or morphology of resting ECG (eg, complete left bundle branch block, third-degree heart block) (c). Any factors that increase the risk of QTc prolongation or risk of arrhythmic events (d). Experience of any of the following procedures or conditions in the preceding 6 months: coronary artery bypass graft, angioplasty, vascular stent, myocardial infarction, unstable angina pectoris, congestive heart failure New York Heart Association (NYHA) grade ≥ 2 (e). Uncontrolled hypotension (f) uncontrolled hypertension (g). Cardiac ejection fraction outside institutional range of normal or \< 50% (whichever is higher) 7. uncontrolled or high grade or symptomatic arrhythmia and atrial fibrillation 8. Any of these clinically significant abnormalities of glucose metabolism at screening: 1. . diabetes mellitus type I or type II requiring insulin treatment 2. . Glycated haemoglobin (HbA1c) ≥ 8.0% (63.9 mmol/mol) 9. Previous allogeneic bone marrow transplant or solid organ transplant. Key exclusion criteria for the phase III only: 1. Any prior treatment with, AKT, PI3K or mTOR inhibitors. 2. Prior treatment with CDK4/6 inhibitors in the metastatic setting (prior CDK4/6 inhibitors permitted in the adjuvant setting provided there was a CDK4/6i treatment free interval of at least 12 months). 3. More than 1 line of chemotherapy for metastatic disease. 4. Any line of endocrine-based therapy for inoperable locally advanced or metastatic disease.