Inclusion Criteria:
1. Histological diagnosis of metastatic or inoperable locally advanced ER positive/HER2 negative breast cancer. Assessment of ER and HER2 status as per local assessment. Histologically proven primary ER+ (Allred score 3/8 or greater, or stain in more than 1% of cancer cells) and HER2- (immunohistochemistry 0/1+ or negative by in situ hybridization) breast cancer as determined by local laboratory.
2. Willingness to consent for an archival tumour tissue sample (of advanced disease) to be requested for transfer to the Royal Marsden during study screening for future analysis. Patients without a metastatic biopsy are eligible if archival tumour from the breast primary tumour is available, but only after discussion with the Chief Investigator (see section 7.3.1). (PI assessment that a biopsy is not clinically appropriate will be required as evidence before discussion with the CI).
3. Previously treated with no more than one prior line of chemotherapy for advanced disease.
4. Patients eligible according to standard of care for fulvestrant in combination with a CDK4/6 inhibitor (abemaciclib, palbociclib, or ribociclib).
5. Patients must have progressed on or within 1 month from stopping prior endocrine therapy for advanced disease, or relapsed on or within 12 months of completing adjuvant endocrine therapy.
6. Measurable disease according to RECIST 1.1 or assessable bone disease (lytic or mixed lytic/sclerotic).
7. Eastern Cooperative Oncology Group (ECOG) performance status of 0, 1, or 2.
8. Adequate bone marrow, renal, and liver function within 14 days prior to the first study treatment on Day 1 of Cycle 1, defined as:
* Neutrophils (ANC \>= 2000/uL), haemoglobin \>= 90 g/L, platelet count \>= 100 x 10\^9/L
* Serum albumin \>= 3 g/dL
* Total bilirubin \<= 1.5 times the upper limit of normal (ULN). Patients with known Gilbert syndrome may be enrolled if bilirubin \<= 3 times ULN
* AST and ALT \<= 2.5 times ULN. Patients with documented liver or bone metastases may have AST and ALT \<= 5 times ULN
* ALP \<= 2 times ULN. Patients with known liver involvement may have ALP \<= 5 times ULN. Patients with known bone involvement may have ALP \<= 7 times ULN
* Serum creatinine \<= 1.5 times ULN or creatinine clearance \>= 50 mL/min using the Cockcroft-Gault formula
* INR \< 1.5 times ULN and aPTT \< 1.5 times ULN. Patients requiring anticoagulation should receive low-molecular-weight heparin or a direct oral anticoagulant
9. Fasting glucose \<= 150 mg/dL and HbA1c \<= 7.5%.
10. Negative serum pregnancy test at screening for females of childbearing potential.
11. Patients able to have children must agree to use a highly effective method of contraception (failure rate less than 1% per year) throughout the study and for at least two years after the last dose of fulvestrant and 90 days after the last dose of palbociclib or ipatasertib. Patients must also agree to refrain from donating eggs or sperm during this period.
12. Pre- or peri-menopausal patients must be treated with licensed GnRH analogues as per standard of care.
13. Aged 18 years or older.
14. Written informed consent has been provided, signed and dated.
Exclusion Criteria:
1. Prior exposure to adjuvant CDK4/6 inhibitors (abemaciclib, palbociclib, or ribociclib) for early breast cancer less than 12 months (52 weeks or 365 days) prior to breast cancer recurrence.
2. Prior treatment with fulvestrant for advanced breast cancer.
3. Prior treatment with an AKT inhibitor, PIK3CA inhibitor, or mTOR inhibitor in any setting.
4. History of malabsorption syndrome or other condition that would interfere with enteral absorption, or inability or unwillingness to swallow oral medication.
5. Systemic chemotherapy within 14 days or endocrine therapy within 7 days prior to registration.
6. Major surgery within 4 weeks prior to registration.
7. Palliative radiotherapy within 14 days prior to registration.
8. Known leptomeningeal disease, untreated brain metastases, spinal cord compression, or symptomatic brain metastases requiring steroids.
9. Clinically significant, uncontrolled cardiac disease or cardiac repolarization abnormality, including but not limited to:
* Angina pectoris, symptomatic pericarditis, coronary artery bypass graft, or myocardial infarction within 12 months prior to study entry
* Symptomatic cardiac failure (NYHA class II to IV or LVEF \< 50%), uncontrolled hypertension, cardiac dysrhythmia requiring medication, significant or symptomatic bradycardia, long QT syndrome, family history of congenital long QT syndrome or idiopathic sudden death
* Cerebrovascular accident or transient ischemic attack within 12 months
* Known risk factors for prolonged QT interval or Torsade de Pointes
* Uncorrected hypomagnesaemia or hypokalaemia of Grade 3 or higher
* Systolic blood pressure \> 160 mmHg or \< 90 mmHg
* Resting heart rate \< 50 beats per minute
* Screening QTcF \> 470 ms based on the mean of three ECGs
10. Lung disease including any history of pneumonitis, interstitial lung disease, idiopathic pulmonary fibrosis, cystic fibrosis, aspergillosis, active tuberculosis, or opportunistic infections such as pneumocystis pneumonia or cytomegalovirus pneumonia.
11. Uncontrolled pleural effusion, pericardial effusion, or ascites as judged by the investigator.
12. Type I or II diabetes requiring insulin therapy.
13. Use of potent CYP3A4 inducers or inhibitors within 2 weeks or five elimination half-lives (whichever is longer) prior to the first dose of palbociclib with or without ipatasertib.
14. Known HIV infection or AIDS-related illness.
15. Active infection requiring systemic therapy.
16. Known acute or chronic hepatitis B or C infection.
* Patients with resolved hepatitis B infection (HBsAg negative, HBcAb positive, and HBV DNA negative) are eligible
* Patients positive for HCV antibody are eligible only if HCV RNA by PCR is negative
17. Clinically significant liver disease consistent with Child-Pugh class B or C.
18. Administration of a live vaccine within 4 weeks prior to study entry.
19. Diagnosis of another malignancy within 5 years, except for adequately treated basal cell carcinoma, squamous cell carcinoma of the skin, or carcinoma in situ of the breast or cervix.
20. Participation in another study involving investigational drugs within 4 weeks prior to study entry or during study participation.
21. Persisting toxicity related to prior therapy greater than Grade 1, except stable peripheral neuropathy Grade 2 or alopecia Grade 2.
22. Other severe acute or chronic medical condition or laboratory abnormality that may increase the risk associated with study participation or interfere with interpretation of results, including colitis, inflammatory bowel disease, active bowel inflammation (for example diverticulitis), psychiatric illness, recent or active suicidal ideation or behaviour, or end-stage renal disease requiring haemodialysis.
23. Known allergy or hypersensitivity to ipatasertib, palbociclib, fulvestrant, or any of their components.
24. Pregnancy or breastfeeding.
25. Requirement for chronic corticosteroid therapy greater than 10 mg prednisolone per day, or equivalent doses of other systemic corticosteroids or immunosuppressants for chronic disease.