AKT Inhibitor, Ipatasertib, With Endocrine and CDK 4/6 Inhibitor for Patients With Metastatic Breast Cancer (TAKTIC)

Inclusion Criteria: * Adult women (≥ 18 years of age) with biopsy proven HR+/HER2 negative breast cancer; HR+ defined as ≥1% positivity for ER, and/or PR (≥1%), as per local assessment. HER2 as per standard CAP guidelines (local assessment). * Postmenopausal women with locally advanced or metastatic BC. Patients must be postmenopausal women as defined by one of the following: * Women \>60 years OR * Women ≤60 years, and any one of following: * LH and FSH level in the postmenopausal range according to institutional standards * s/p post bilateral surgical oophorectomy. * Premenopausal/perimenopausal women on gonadotropin-releasing hormone agonist (to be continued during study) and estradiol level in the postmenopausal range according to institutional standards * Disease progression on at least one prior therapy for metastatic disease, including endocrine therapy with/without CDK 4/6 inhibitor (palbociclib or ribociclib or abemaciclib). Disease recurrence during/within 12 month of (neo)adjuvant endocrine therapy (with/without CDK 4/6 inhibitor) will count as one prior therapy for this definition. * ECOG Performance Status 0 - 2 * Left ventricular ejection fraction (LVEF) ≥ 50% * Evaluable or measurable disease: at least one lesion that can be accurately measured in at least one dimension ≥ 20 mm with conventional imaging techniques or ≥ 10 mm with spiral CT or MRI. Bone lesions in the absence of measurable disease as defined above is also acceptable. * Discontinuation of prior breast cancer therapies, including endocrine therapy, for 14 days (non-myelosuppressive) or 21 days (myelosuppressive). Wash-out for Fulvestrant and tamoxifen will be 28 days. * Prior mTOR inhibitor and/or PI3K inhibitor allowed (all arms) * Prior aromatase inhibitor is allowed (all arms) * Adequate bone marrow function: ANC ≥ 1000/mm3, hemoglobin ≥9 g/dl, and platelets ≥ 100,000/mm3. * Adequate hepatic function: Total bilirubin \< 1.5mg/dL, AST and ALT \< 3X Institutional ULN (or 5 X Institutional ULN in presence of hepatic mets). * Adequate renal function: Calculated creatinine clearance ≥ 30 mL/min * Fasting blood glucose \<140 mg/dL, and hemoglobin A1c \<7. * Signed informed consent and agree to comply with study procedures. Exclusion Criteria: * Participants with progressive CNS metastatic disease. Patients with stable CNS metastasis would be eligible, provided mets radiologically stable for atleast one month, and patient is not actively taking steroids. * Participants who have had chemotherapy or radiotherapy within 4 weeks (6 weeks for nitrosoureas or mitomycin C) prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier. * Prior use of AKT inhibitor (any setting) * Treatment with strong CYP3A inhibitors or strong CYP3A inducers within 14 days or 5 drug-elimination half-lives, whichever is longer, prior to initiation of study treatment. Because the lists of these agents are constantly changing, it is important to regularly consult a frequently-updated list such as http://medicine.iupui.edu/clinpharm/ddis/table.aspx; medical reference texts such as the Physicians' Desk Reference may also provide this information. As part of the enrollment/informed consent procedures, the patient will be counseled on the risk of interactions with other agents, and what to do if new medications need to be prescribed or if the patient is considering a new over-the-counter medicine or herbal product. * Uncontrolled inter-current illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements. Patient has impairment of gastrointestinal (GI) function or GI disease that may significantly alter the absorption of the study drugs (e.g., inflammatory bowel disease, ulcerative diseases, uncontrolled nausea, vomiting, diarrhea, malabsorption syndrome, or small bowel resection). * Clinically significant, uncontrolled heart disease and/or cardiac repolarization abnormality including any of the following: * History of angina pectoris, symptomatic pericarditis, coronary artery bypass graft (CABG) or myocardial infarction within 6 months prior to study entry. * Documented cardiomyopathy. * History of cardiac failure, significant/symptomatic bradycardia, Long QT syndrome, family history of idiopathic sudden death or congenital long QT syndrome or any of the following: * Known risk to prolong the QT interval or induce Torsade's de Pointes. * Uncorrected hypomagnesemia or hypokalemia. * Systolic Blood Pressure (SBP) \>160 mmHg or \<90 mmHg. * Bradycardia (heart rate \<50 at rest), by ECG or pulse. * On screening, inability to determine the QTcF interval on the ECG (i.e.: unreadable or not interpretable) or QTcF \>450 screening ECG (based on a mean of 3 ECGs). * HIV-positive participants on combination antiretroviral therapy are ineligible. These participants are at increased risk of lethal infections when treated with marrow-suppressive therapy. Appropriate studies will be undertaken in participants receiving combination antiretroviral therapy when indicated. * History of Type I or Type II diabetes mellitus requiring insulin. Patients who are on a stable dose of oral diabetes medication ≥ 2 weeks prior to initiation of study treatment are eligible for enrollment. Patients must meet the laboratory eligibility criteria for fasting blood glucose and hemoglobin A1c as outlined in the inclusion criteria. * Pregnant women are excluded from this study because the safety of study medications is not established in pregnant women. * Women of child-bearing potential, defined as all women physiologically capable of becoming pregnant, unless they are using highly effective methods of contraception throughout the study and for 8 weeks after study drug discontinuation. Women are considered post-menopausal and not of child bearing potential if they have had 12 months of natural (spontaneous) amenorrhea with an appropriate clinical profile (e.g. age appropriate, history of vasomotor symptoms) or have had surgical bilateral oophorectomy (with or without hysterectomy) or tubal ligation at least six weeks ago. In the case of bilateral oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment is she considered not of child bearing potential. Highly effective contraception methods include: * Total abstinence when this is in line with the preferred and usual lifestyle of the patient. Periodic abstinence (e.g., calendar, ovulation, symptothermal, post-ovulation methods) and withdrawal are not acceptable methods of contraception * Female sterilization (have had surgical bilateral oophorectomy with or without hysterectomy), total hysterectomy, or tubal ligation at least six weeks before taking study treatment. In case of oophorectomy alone, only when the reproductive status of the woman has been confirmed by follow up hormone level assessment * Use of oral, injected or implanted hormonal methods of contraception or placement of an intrauterine device (IUD) or intrauterine system (IUS), or other forms of hormonal contraception that have comparable efficacy (failure rate \<1%), for example hormone vaginal ring or transdermal hormone contraception. * In case of use of oral contraception, women should have been stable on the same pill for a minimum of 3 months before taking study treatment. Note: While oral contraceptives are allowed, they should be used in conjunction with a barrier method of contraception due to unknown effect of drug-drug interaction. * For Arm A only: patients who have received prior fulvestrant. * For Arm C only: h/o of intolerable toxicity to CDK 4/6 inhibitor resulting in treatment discontinuation due to toxicity